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VisSim_3dCubes_Rotate_v0

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Visual Manipulation 1

easy_0000

A

easy

{"question_id": "easy_0000", "num_cubes": 4, "difficulty": "easy", "rotation_task": {"axis": "y", "angle": 180, "direction": "clockwise"}, "color_mode": "multiple", "options": {"A": {"axis": "y", "angle": 180, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "z", "angle": 60, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 90, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "y", "angle": 90, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "A", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 180\u00b0 clockwise around the Y axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.7812388227027043, 0.8628560274087655, 0.0847223113648985], [0.7812388227027043, 0.8628560274087655, 0.0847223113648985], [0.7812388227027043, 0.8628560274087655, 0.0847223113648985], [0.7812388227027043, 0.8628560274087655, 0.0847223113648985], [0.7812388227027043, 0.8628560274087655, 0.0847223113648985], [0.7812388227027043, 0.8628560274087655, 0.0847223113648985], [0.2338647386386537, 0.17991155053696561, 0.9826680838822196], [0.2338647386386537, 0.17991155053696561, 0.9826680838822196], [0.2338647386386537, 0.17991155053696561, 0.9826680838822196], [0.2338647386386537, 0.17991155053696561, 0.9826680838822196], [0.2338647386386537, 0.17991155053696561, 0.9826680838822196], [0.2338647386386537, 0.17991155053696561, 0.9826680838822196], [0.45293312251237117, 0.9414369610211865, 0.23453824503303633], [0.45293312251237117, 0.9414369610211865, 0.23453824503303633], [0.45293312251237117, 0.9414369610211865, 0.23453824503303633], [0.45293312251237117, 0.9414369610211865, 0.23453824503303633], [0.45293312251237117, 0.9414369610211865, 0.23453824503303633], [0.45293312251237117, 0.9414369610211865, 0.23453824503303633]]}

easy_0001

D

easy

{"question_id": "easy_0001", "num_cubes": 2, "difficulty": "easy", "rotation_task": {"axis": "z", "angle": 60, "direction": "counter-clockwise"}, "color_mode": "multiple", "options": {"A": {"axis": "x", "angle": 30, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "x", "angle": 60, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "y", "angle": 90, "direction": "clockwise", "filename": "choice2.png"}, "D": {"axis": "z", "angle": 60, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "D", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 60\u00b0 counter-clockwise around the Z axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.6856295269958266, 0.8184798821296311, 0.32785914040269204], [0.6856295269958266, 0.8184798821296311, 0.32785914040269204], [0.6856295269958266, 0.8184798821296311, 0.32785914040269204], [0.6856295269958266, 0.8184798821296311, 0.32785914040269204], [0.6856295269958266, 0.8184798821296311, 0.32785914040269204], [0.6856295269958266, 0.8184798821296311, 0.32785914040269204], [0.9777390836298916, 0.3527158078461152, 0.2092387209494304], [0.9777390836298916, 0.3527158078461152, 0.2092387209494304], [0.9777390836298916, 0.3527158078461152, 0.2092387209494304], [0.9777390836298916, 0.3527158078461152, 0.2092387209494304], [0.9777390836298916, 0.3527158078461152, 0.2092387209494304], [0.9777390836298916, 0.3527158078461152, 0.2092387209494304]]}

easy_0002

C

easy

{"question_id": "easy_0002", "num_cubes": 2, "difficulty": "easy", "rotation_task": {"axis": "x", "angle": 30, "direction": "clockwise"}, "color_mode": "multiple", "options": {"A": {"axis": "y", "angle": 60, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "z", "angle": 60, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 30, "direction": "clockwise", "filename": "choice2.png"}, "D": {"axis": "y", "angle": 180, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "C", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 30\u00b0 clockwise around the X axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.9029439173987545, 0.7465368233714931, 0.03989330470821861], [0.9029439173987545, 0.7465368233714931, 0.03989330470821861], [0.9029439173987545, 0.7465368233714931, 0.03989330470821861], [0.9029439173987545, 0.7465368233714931, 0.03989330470821861], [0.9029439173987545, 0.7465368233714931, 0.03989330470821861], [0.9029439173987545, 0.7465368233714931, 0.03989330470821861], [0.407417027493981, 0.5339221201829438, 0.957395235569946], [0.407417027493981, 0.5339221201829438, 0.957395235569946], [0.407417027493981, 0.5339221201829438, 0.957395235569946], [0.407417027493981, 0.5339221201829438, 0.957395235569946], [0.407417027493981, 0.5339221201829438, 0.957395235569946], [0.407417027493981, 0.5339221201829438, 0.957395235569946]]}

easy_0003

B

easy

{"question_id": "easy_0003", "num_cubes": 3, "difficulty": "easy", "rotation_task": {"axis": "z", "angle": 120, "direction": "counter-clockwise"}, "color_mode": "multiple", "options": {"A": {"axis": "x", "angle": 150, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "z", "angle": 120, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 120, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "y", "angle": 120, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "B", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 120\u00b0 counter-clockwise around the Z axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.32822241504644, 0.9477153052373396, 0.3679438085049438], [0.32822241504644, 0.9477153052373396, 0.3679438085049438], [0.32822241504644, 0.9477153052373396, 0.3679438085049438], [0.32822241504644, 0.9477153052373396, 0.3679438085049438], [0.32822241504644, 0.9477153052373396, 0.3679438085049438], [0.32822241504644, 0.9477153052373396, 0.3679438085049438], [0.9138713455989644, 0.5064255397250882, 0.06467818206611164], [0.9138713455989644, 0.5064255397250882, 0.06467818206611164], [0.9138713455989644, 0.5064255397250882, 0.06467818206611164], [0.9138713455989644, 0.5064255397250882, 0.06467818206611164], [0.9138713455989644, 0.5064255397250882, 0.06467818206611164], [0.9138713455989644, 0.5064255397250882, 0.06467818206611164], [0.7127301999892546, 0.19563064072265868, 0.8629305455782355], [0.7127301999892546, 0.19563064072265868, 0.8629305455782355], [0.7127301999892546, 0.19563064072265868, 0.8629305455782355], [0.7127301999892546, 0.19563064072265868, 0.8629305455782355], [0.7127301999892546, 0.19563064072265868, 0.8629305455782355], [0.7127301999892546, 0.19563064072265868, 0.8629305455782355]]}

easy_0004

D

easy

{"question_id": "easy_0004", "num_cubes": 2, "difficulty": "easy", "rotation_task": {"axis": "z", "angle": 180, "direction": "clockwise"}, "color_mode": "multiple", "options": {"A": {"axis": "z", "angle": 120, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 150, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "y", "angle": 60, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "z", "angle": 180, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "D", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 180\u00b0 clockwise around the Z axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.44340120467669775, 0.8313605532228856, 0.08540423885909965], [0.44340120467669775, 0.8313605532228856, 0.08540423885909965], [0.44340120467669775, 0.8313605532228856, 0.08540423885909965], [0.44340120467669775, 0.8313605532228856, 0.08540423885909965], [0.44340120467669775, 0.8313605532228856, 0.08540423885909965], [0.44340120467669775, 0.8313605532228856, 0.08540423885909965], [0.3624402477040625, 0.11907975550654981, 0.6815903145527974], [0.3624402477040625, 0.11907975550654981, 0.6815903145527974], [0.3624402477040625, 0.11907975550654981, 0.6815903145527974], [0.3624402477040625, 0.11907975550654981, 0.6815903145527974], [0.3624402477040625, 0.11907975550654981, 0.6815903145527974], [0.3624402477040625, 0.11907975550654981, 0.6815903145527974]]}

easy_0005

D

easy

{"question_id": "easy_0005", "num_cubes": 4, "difficulty": "easy", "rotation_task": {"axis": "z", "angle": 120, "direction": "counter-clockwise"}, "color_mode": "multiple", "options": {"A": {"axis": "x", "angle": 180, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "x", "angle": 90, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "z", "angle": 30, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "z", "angle": 120, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "D", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 120\u00b0 counter-clockwise around the Z axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.9309794722391862, 0.151788227957655, 0.7255980073941526], [0.9309794722391862, 0.151788227957655, 0.7255980073941526], [0.9309794722391862, 0.151788227957655, 0.7255980073941526], [0.9309794722391862, 0.151788227957655, 0.7255980073941526], [0.9309794722391862, 0.151788227957655, 0.7255980073941526], [0.9309794722391862, 0.151788227957655, 0.7255980073941526], [0.9651435282453662, 0.2712041869102261, 0.16410766339928262], [0.9651435282453662, 0.2712041869102261, 0.16410766339928262], [0.9651435282453662, 0.2712041869102261, 0.16410766339928262], [0.9651435282453662, 0.2712041869102261, 0.16410766339928262], [0.9651435282453662, 0.2712041869102261, 0.16410766339928262], [0.9651435282453662, 0.2712041869102261, 0.16410766339928262], [0.18222592616002342, 0.6793595926827114, 0.47334841591497656], [0.18222592616002342, 0.6793595926827114, 0.47334841591497656], [0.18222592616002342, 0.6793595926827114, 0.47334841591497656], [0.18222592616002342, 0.6793595926827114, 0.47334841591497656], [0.18222592616002342, 0.6793595926827114, 0.47334841591497656], [0.18222592616002342, 0.6793595926827114, 0.47334841591497656]]}

easy_0006

A

easy

{"question_id": "easy_0006", "num_cubes": 3, "difficulty": "easy", "rotation_task": {"axis": "z", "angle": 60, "direction": "clockwise"}, "color_mode": "multiple", "options": {"A": {"axis": "z", "angle": 60, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 180, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "y", "angle": 120, "direction": "clockwise", "filename": "choice2.png"}, "D": {"axis": "x", "angle": 150, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "A", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 60\u00b0 clockwise around the Z axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.8447368713838769, 0.15896186445237503, 0.5848650904929762], [0.8447368713838769, 0.15896186445237503, 0.5848650904929762], [0.8447368713838769, 0.15896186445237503, 0.5848650904929762], [0.8447368713838769, 0.15896186445237503, 0.5848650904929762], [0.8447368713838769, 0.15896186445237503, 0.5848650904929762], [0.8447368713838769, 0.15896186445237503, 0.5848650904929762], [0.0931723179727911, 0.9903349031635904, 0.039107420524362224], [0.0931723179727911, 0.9903349031635904, 0.039107420524362224], [0.0931723179727911, 0.9903349031635904, 0.039107420524362224], [0.0931723179727911, 0.9903349031635904, 0.039107420524362224], [0.0931723179727911, 0.9903349031635904, 0.039107420524362224], [0.0931723179727911, 0.9903349031635904, 0.039107420524362224], [0.19728756936159783, 0.05533378512340126, 0.7713605970472233], [0.19728756936159783, 0.05533378512340126, 0.7713605970472233], [0.19728756936159783, 0.05533378512340126, 0.7713605970472233], [0.19728756936159783, 0.05533378512340126, 0.7713605970472233], [0.19728756936159783, 0.05533378512340126, 0.7713605970472233], [0.19728756936159783, 0.05533378512340126, 0.7713605970472233]]}

easy_0007

A

easy

{"question_id": "easy_0007", "num_cubes": 2, "difficulty": "easy", "rotation_task": {"axis": "y", "angle": 90, "direction": "counter-clockwise"}, "color_mode": "multiple", "options": {"A": {"axis": "y", "angle": 90, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "z", "angle": 150, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "y", "angle": 120, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "z", "angle": 180, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "A", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 90\u00b0 counter-clockwise around the Y axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.746619077714701, 0.2843505137878707, 0.07318592682445602], [0.746619077714701, 0.2843505137878707, 0.07318592682445602], [0.746619077714701, 0.2843505137878707, 0.07318592682445602], [0.746619077714701, 0.2843505137878707, 0.07318592682445602], [0.746619077714701, 0.2843505137878707, 0.07318592682445602], [0.746619077714701, 0.2843505137878707, 0.07318592682445602], [0.17915211695887734, 0.2252149639010555, 0.6213876494733358], [0.17915211695887734, 0.2252149639010555, 0.6213876494733358], [0.17915211695887734, 0.2252149639010555, 0.6213876494733358], [0.17915211695887734, 0.2252149639010555, 0.6213876494733358], [0.17915211695887734, 0.2252149639010555, 0.6213876494733358], [0.17915211695887734, 0.2252149639010555, 0.6213876494733358]]}

easy_0008

B

easy

{"question_id": "easy_0008", "num_cubes": 4, "difficulty": "easy", "rotation_task": {"axis": "y", "angle": 180, "direction": "counter-clockwise"}, "color_mode": "multiple", "options": {"A": {"axis": "z", "angle": 90, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 180, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "z", "angle": 90, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "x", "angle": 30, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "B", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 180\u00b0 counter-clockwise around the Y axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.507860285219258, 0.3247760106164139, 0.782783932287221], [0.507860285219258, 0.3247760106164139, 0.782783932287221], [0.507860285219258, 0.3247760106164139, 0.782783932287221], [0.507860285219258, 0.3247760106164139, 0.782783932287221], [0.507860285219258, 0.3247760106164139, 0.782783932287221], [0.507860285219258, 0.3247760106164139, 0.782783932287221], [0.9011694110903482, 0.0681034081542059, 0.9254473201496042], [0.9011694110903482, 0.0681034081542059, 0.9254473201496042], [0.9011694110903482, 0.0681034081542059, 0.9254473201496042], [0.9011694110903482, 0.0681034081542059, 0.9254473201496042], [0.9011694110903482, 0.0681034081542059, 0.9254473201496042], [0.9011694110903482, 0.0681034081542059, 0.9254473201496042], [0.8967810896628827, 0.23290890657044772, 0.9980189767292871], [0.8967810896628827, 0.23290890657044772, 0.9980189767292871], [0.8967810896628827, 0.23290890657044772, 0.9980189767292871], [0.8967810896628827, 0.23290890657044772, 0.9980189767292871], [0.8967810896628827, 0.23290890657044772, 0.9980189767292871], [0.8967810896628827, 0.23290890657044772, 0.9980189767292871], [0.022297039921920114, 0.864128320345446, 0.8317059167512483], [0.022297039921920114, 0.864128320345446, 0.8317059167512483], [0.022297039921920114, 0.864128320345446, 0.8317059167512483], [0.022297039921920114, 0.864128320345446, 0.8317059167512483], [0.022297039921920114, 0.864128320345446, 0.8317059167512483], [0.022297039921920114, 0.864128320345446, 0.8317059167512483]]}

easy_0009

B

easy

{"question_id": "easy_0009", "num_cubes": 2, "difficulty": "easy", "rotation_task": {"axis": "y", "angle": 180, "direction": "counter-clockwise"}, "color_mode": "multiple", "options": {"A": {"axis": "x", "angle": 150, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 180, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "y", "angle": 150, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "z", "angle": 60, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "B", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 180\u00b0 counter-clockwise around the Y axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.1854058048116105, 0.5511635711230289, 0.6956937343277578], [0.1854058048116105, 0.5511635711230289, 0.6956937343277578], [0.1854058048116105, 0.5511635711230289, 0.6956937343277578], [0.1854058048116105, 0.5511635711230289, 0.6956937343277578], [0.1854058048116105, 0.5511635711230289, 0.6956937343277578], [0.1854058048116105, 0.5511635711230289, 0.6956937343277578], [0.22072066334155316, 0.9955020067041161, 0.8360435213979531], [0.22072066334155316, 0.9955020067041161, 0.8360435213979531], [0.22072066334155316, 0.9955020067041161, 0.8360435213979531], [0.22072066334155316, 0.9955020067041161, 0.8360435213979531], [0.22072066334155316, 0.9955020067041161, 0.8360435213979531], [0.22072066334155316, 0.9955020067041161, 0.8360435213979531]]}

easy_0010

D

easy

{"question_id": "easy_0010", "num_cubes": 4, "difficulty": "easy", "rotation_task": {"axis": "z", "angle": 180, "direction": "counter-clockwise"}, "color_mode": "multiple", "options": {"A": {"axis": "x", "angle": 60, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 120, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "y", "angle": 60, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "z", "angle": 180, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "D", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 180\u00b0 counter-clockwise around the Z axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.3416833935088508, 0.9772643694236705, 0.8793704838445855], [0.3416833935088508, 0.9772643694236705, 0.8793704838445855], [0.3416833935088508, 0.9772643694236705, 0.8793704838445855], [0.3416833935088508, 0.9772643694236705, 0.8793704838445855], [0.3416833935088508, 0.9772643694236705, 0.8793704838445855], [0.3416833935088508, 0.9772643694236705, 0.8793704838445855], [0.9577314268602709, 0.6854716268057552, 0.36569307937640494], [0.9577314268602709, 0.6854716268057552, 0.36569307937640494], [0.9577314268602709, 0.6854716268057552, 0.36569307937640494], [0.9577314268602709, 0.6854716268057552, 0.36569307937640494], [0.9577314268602709, 0.6854716268057552, 0.36569307937640494], [0.9577314268602709, 0.6854716268057552, 0.36569307937640494], [0.3531177544571691, 0.6257196590150365, 0.9595295619065938], [0.3531177544571691, 0.6257196590150365, 0.9595295619065938], [0.3531177544571691, 0.6257196590150365, 0.9595295619065938], [0.3531177544571691, 0.6257196590150365, 0.9595295619065938], [0.3531177544571691, 0.6257196590150365, 0.9595295619065938], [0.3531177544571691, 0.6257196590150365, 0.9595295619065938]]}

easy_0011

B

easy

{"question_id": "easy_0011", "num_cubes": 4, "difficulty": "easy", "rotation_task": {"axis": "z", "angle": 150, "direction": "counter-clockwise"}, "color_mode": "multiple", "options": {"A": {"axis": "z", "angle": 90, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "z", "angle": 150, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "y", "angle": 90, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "x", "angle": 30, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "B", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 150\u00b0 counter-clockwise around the Z axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.9384072363756426, 0.2195271674589817, 0.9962508643654585], [0.9384072363756426, 0.2195271674589817, 0.9962508643654585], [0.9384072363756426, 0.2195271674589817, 0.9962508643654585], [0.9384072363756426, 0.2195271674589817, 0.9962508643654585], [0.9384072363756426, 0.2195271674589817, 0.9962508643654585], [0.9384072363756426, 0.2195271674589817, 0.9962508643654585], [0.2987113847437739, 0.6673953270896752, 0.8145570107051807], [0.2987113847437739, 0.6673953270896752, 0.8145570107051807], [0.2987113847437739, 0.6673953270896752, 0.8145570107051807], [0.2987113847437739, 0.6673953270896752, 0.8145570107051807], [0.2987113847437739, 0.6673953270896752, 0.8145570107051807], [0.2987113847437739, 0.6673953270896752, 0.8145570107051807], [0.7069564999704955, 0.2860824927100821, 0.20463854742951948], [0.7069564999704955, 0.2860824927100821, 0.20463854742951948], [0.7069564999704955, 0.2860824927100821, 0.20463854742951948], [0.7069564999704955, 0.2860824927100821, 0.20463854742951948], [0.7069564999704955, 0.2860824927100821, 0.20463854742951948], [0.7069564999704955, 0.2860824927100821, 0.20463854742951948], [0.8329315107908071, 0.3926944936527279, 0.6279831277902315], [0.8329315107908071, 0.3926944936527279, 0.6279831277902315], [0.8329315107908071, 0.3926944936527279, 0.6279831277902315], [0.8329315107908071, 0.3926944936527279, 0.6279831277902315], [0.8329315107908071, 0.3926944936527279, 0.6279831277902315], [0.8329315107908071, 0.3926944936527279, 0.6279831277902315]]}

easy_0012

C

easy

{"question_id": "easy_0012", "num_cubes": 3, "difficulty": "easy", "rotation_task": {"axis": "x", "angle": 30, "direction": "counter-clockwise"}, "color_mode": "multiple", "options": {"A": {"axis": "y", "angle": 180, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 90, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 30, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "y", "angle": 120, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "C", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 30\u00b0 counter-clockwise around the X axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.8857581966471992, 0.46097461498833714, 0.5683702270461032], [0.8857581966471992, 0.46097461498833714, 0.5683702270461032], [0.8857581966471992, 0.46097461498833714, 0.5683702270461032], [0.8857581966471992, 0.46097461498833714, 0.5683702270461032], [0.8857581966471992, 0.46097461498833714, 0.5683702270461032], [0.8857581966471992, 0.46097461498833714, 0.5683702270461032], [0.9521744227931205, 0.03045568461247289, 0.021269359612123395], [0.9521744227931205, 0.03045568461247289, 0.021269359612123395], [0.9521744227931205, 0.03045568461247289, 0.021269359612123395], [0.9521744227931205, 0.03045568461247289, 0.021269359612123395], [0.9521744227931205, 0.03045568461247289, 0.021269359612123395], [0.9521744227931205, 0.03045568461247289, 0.021269359612123395], [0.680499791288193, 0.189358617803411, 0.45766895222270154], [0.680499791288193, 0.189358617803411, 0.45766895222270154], [0.680499791288193, 0.189358617803411, 0.45766895222270154], [0.680499791288193, 0.189358617803411, 0.45766895222270154], [0.680499791288193, 0.189358617803411, 0.45766895222270154], [0.680499791288193, 0.189358617803411, 0.45766895222270154]]}

easy_0013

A

easy

{"question_id": "easy_0013", "num_cubes": 3, "difficulty": "easy", "rotation_task": {"axis": "z", "angle": 60, "direction": "clockwise"}, "color_mode": "multiple", "options": {"A": {"axis": "z", "angle": 60, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 30, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "z", "angle": 90, "direction": "clockwise", "filename": "choice2.png"}, "D": {"axis": "x", "angle": 30, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "A", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 60\u00b0 clockwise around the Z axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.9313399015974583, 0.302589728825028, 0.3726402511394044], [0.9313399015974583, 0.302589728825028, 0.3726402511394044], [0.9313399015974583, 0.302589728825028, 0.3726402511394044], [0.9313399015974583, 0.302589728825028, 0.3726402511394044], [0.9313399015974583, 0.302589728825028, 0.3726402511394044], [0.9313399015974583, 0.302589728825028, 0.3726402511394044], [0.15334206662374616, 0.19324502019775047, 0.8724438056898074], [0.15334206662374616, 0.19324502019775047, 0.8724438056898074], [0.15334206662374616, 0.19324502019775047, 0.8724438056898074], [0.15334206662374616, 0.19324502019775047, 0.8724438056898074], [0.15334206662374616, 0.19324502019775047, 0.8724438056898074], [0.15334206662374616, 0.19324502019775047, 0.8724438056898074]]}

easy_0014

B

easy

{"question_id": "easy_0014", "num_cubes": 3, "difficulty": "easy", "rotation_task": {"axis": "z", "angle": 90, "direction": "counter-clockwise"}, "color_mode": "multiple", "options": {"A": {"axis": "x", "angle": 180, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "z", "angle": 90, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 150, "direction": "clockwise", "filename": "choice2.png"}, "D": {"axis": "x", "angle": 90, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "B", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 90\u00b0 counter-clockwise around the Z axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.7979394593210316, 0.31103330426466713, 0.44749708459968207], [0.7979394593210316, 0.31103330426466713, 0.44749708459968207], [0.7979394593210316, 0.31103330426466713, 0.44749708459968207], [0.7979394593210316, 0.31103330426466713, 0.44749708459968207], [0.7979394593210316, 0.31103330426466713, 0.44749708459968207], [0.7979394593210316, 0.31103330426466713, 0.44749708459968207], [0.7255116207172643, 0.5068042528552876, 0.14376299716000318], [0.7255116207172643, 0.5068042528552876, 0.14376299716000318], [0.7255116207172643, 0.5068042528552876, 0.14376299716000318], [0.7255116207172643, 0.5068042528552876, 0.14376299716000318], [0.7255116207172643, 0.5068042528552876, 0.14376299716000318], [0.7255116207172643, 0.5068042528552876, 0.14376299716000318], [0.6231610392990329, 0.8593438805984754, 0.41555997986169224], [0.6231610392990329, 0.8593438805984754, 0.41555997986169224], [0.6231610392990329, 0.8593438805984754, 0.41555997986169224], [0.6231610392990329, 0.8593438805984754, 0.41555997986169224], [0.6231610392990329, 0.8593438805984754, 0.41555997986169224], [0.6231610392990329, 0.8593438805984754, 0.41555997986169224]]}

easy_0015

B

easy

{"question_id": "easy_0015", "num_cubes": 2, "difficulty": "easy", "rotation_task": {"axis": "x", "angle": 120, "direction": "counter-clockwise"}, "color_mode": "multiple", "options": {"A": {"axis": "z", "angle": 180, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "x", "angle": 120, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 150, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "y", "angle": 60, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "B", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 120\u00b0 counter-clockwise around the X axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.8483315804822266, 0.9579839466884491, 0.2828845905048395], [0.8483315804822266, 0.9579839466884491, 0.2828845905048395], [0.8483315804822266, 0.9579839466884491, 0.2828845905048395], [0.8483315804822266, 0.9579839466884491, 0.2828845905048395], [0.8483315804822266, 0.9579839466884491, 0.2828845905048395], [0.8483315804822266, 0.9579839466884491, 0.2828845905048395], [0.20859681278445386, 0.6574710642447746, 0.6536677542168108], [0.20859681278445386, 0.6574710642447746, 0.6536677542168108], [0.20859681278445386, 0.6574710642447746, 0.6536677542168108], [0.20859681278445386, 0.6574710642447746, 0.6536677542168108], [0.20859681278445386, 0.6574710642447746, 0.6536677542168108], [0.20859681278445386, 0.6574710642447746, 0.6536677542168108]]}

easy_0016

A

easy

{"question_id": "easy_0016", "num_cubes": 2, "difficulty": "easy", "rotation_task": {"axis": "y", "angle": 120, "direction": "counter-clockwise"}, "color_mode": "multiple", "options": {"A": {"axis": "y", "angle": 120, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 30, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 30, "direction": "clockwise", "filename": "choice2.png"}, "D": {"axis": "z", "angle": 90, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "A", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 120\u00b0 counter-clockwise around the Y axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.9717165026568026, 0.33002604905369626, 0.2575127278327902], [0.9717165026568026, 0.33002604905369626, 0.2575127278327902], [0.9717165026568026, 0.33002604905369626, 0.2575127278327902], [0.9717165026568026, 0.33002604905369626, 0.2575127278327902], [0.9717165026568026, 0.33002604905369626, 0.2575127278327902], [0.9717165026568026, 0.33002604905369626, 0.2575127278327902], [0.646214199920148, 0.186537309118592, 0.6203958768297906], [0.646214199920148, 0.186537309118592, 0.6203958768297906], [0.646214199920148, 0.186537309118592, 0.6203958768297906], [0.646214199920148, 0.186537309118592, 0.6203958768297906], [0.646214199920148, 0.186537309118592, 0.6203958768297906], [0.646214199920148, 0.186537309118592, 0.6203958768297906]]}

easy_0017

D

easy

{"question_id": "easy_0017", "num_cubes": 4, "difficulty": "easy", "rotation_task": {"axis": "y", "angle": 120, "direction": "clockwise"}, "color_mode": "multiple", "options": {"A": {"axis": "z", "angle": 180, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "x", "angle": 180, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 120, "direction": "clockwise", "filename": "choice2.png"}, "D": {"axis": "y", "angle": 120, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "D", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 120\u00b0 clockwise around the Y axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.7746526511864873, 0.6638902003028686, 0.24137209475649524], [0.7746526511864873, 0.6638902003028686, 0.24137209475649524], [0.7746526511864873, 0.6638902003028686, 0.24137209475649524], [0.7746526511864873, 0.6638902003028686, 0.24137209475649524], [0.7746526511864873, 0.6638902003028686, 0.24137209475649524], [0.7746526511864873, 0.6638902003028686, 0.24137209475649524], [0.22691204556564926, 0.4204411964622354, 0.762884428164189], [0.22691204556564926, 0.4204411964622354, 0.762884428164189], [0.22691204556564926, 0.4204411964622354, 0.762884428164189], [0.22691204556564926, 0.4204411964622354, 0.762884428164189], [0.22691204556564926, 0.4204411964622354, 0.762884428164189], [0.22691204556564926, 0.4204411964622354, 0.762884428164189], [0.6926492878022424, 0.9805122806347478, 0.2084359519381248], [0.6926492878022424, 0.9805122806347478, 0.2084359519381248], [0.6926492878022424, 0.9805122806347478, 0.2084359519381248], [0.6926492878022424, 0.9805122806347478, 0.2084359519381248], [0.6926492878022424, 0.9805122806347478, 0.2084359519381248], [0.6926492878022424, 0.9805122806347478, 0.2084359519381248], [0.6236742658361607, 0.24578292667408053, 0.18406338636350073], [0.6236742658361607, 0.24578292667408053, 0.18406338636350073], [0.6236742658361607, 0.24578292667408053, 0.18406338636350073], [0.6236742658361607, 0.24578292667408053, 0.18406338636350073], [0.6236742658361607, 0.24578292667408053, 0.18406338636350073], [0.6236742658361607, 0.24578292667408053, 0.18406338636350073]]}

easy_0018

D

easy

{"question_id": "easy_0018", "num_cubes": 2, "difficulty": "easy", "rotation_task": {"axis": "x", "angle": 120, "direction": "counter-clockwise"}, "color_mode": "multiple", "options": {"A": {"axis": "y", "angle": 120, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "z", "angle": 30, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "z", "angle": 180, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "x", "angle": 120, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "D", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 120\u00b0 counter-clockwise around the X axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.7014580419126485, 0.4243670311891519, 0.13637321961529902], [0.7014580419126485, 0.4243670311891519, 0.13637321961529902], [0.7014580419126485, 0.4243670311891519, 0.13637321961529902], [0.7014580419126485, 0.4243670311891519, 0.13637321961529902], [0.7014580419126485, 0.4243670311891519, 0.13637321961529902], [0.7014580419126485, 0.4243670311891519, 0.13637321961529902], [0.42118137563248953, 0.3512240324741176, 0.9206103881316223], [0.42118137563248953, 0.3512240324741176, 0.9206103881316223], [0.42118137563248953, 0.3512240324741176, 0.9206103881316223], [0.42118137563248953, 0.3512240324741176, 0.9206103881316223], [0.42118137563248953, 0.3512240324741176, 0.9206103881316223], [0.42118137563248953, 0.3512240324741176, 0.9206103881316223]]}

easy_0019

D

easy

{"question_id": "easy_0019", "num_cubes": 3, "difficulty": "easy", "rotation_task": {"axis": "z", "angle": 90, "direction": "counter-clockwise"}, "color_mode": "multiple", "options": {"A": {"axis": "z", "angle": 150, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 90, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 30, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "z", "angle": 90, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "D", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 90\u00b0 counter-clockwise around the Z axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.8622430704527568, 0.4280298277343646, 0.6601836924675096], [0.8622430704527568, 0.4280298277343646, 0.6601836924675096], [0.8622430704527568, 0.4280298277343646, 0.6601836924675096], [0.8622430704527568, 0.4280298277343646, 0.6601836924675096], [0.8622430704527568, 0.4280298277343646, 0.6601836924675096], [0.8622430704527568, 0.4280298277343646, 0.6601836924675096], [0.1961606364354671, 0.6586285400854041, 0.5320872999298529], [0.1961606364354671, 0.6586285400854041, 0.5320872999298529], [0.1961606364354671, 0.6586285400854041, 0.5320872999298529], [0.1961606364354671, 0.6586285400854041, 0.5320872999298529], [0.1961606364354671, 0.6586285400854041, 0.5320872999298529], [0.1961606364354671, 0.6586285400854041, 0.5320872999298529], [0.826985494968699, 0.30729809060305024, 0.35629611166174435], [0.826985494968699, 0.30729809060305024, 0.35629611166174435], [0.826985494968699, 0.30729809060305024, 0.35629611166174435], [0.826985494968699, 0.30729809060305024, 0.35629611166174435], [0.826985494968699, 0.30729809060305024, 0.35629611166174435], [0.826985494968699, 0.30729809060305024, 0.35629611166174435]]}

medium_0000

C

medium

{"question_id": "medium_0000", "num_cubes": 4, "difficulty": "medium", "rotation_task": {"axis": "z", "angle": 30, "direction": "clockwise"}, "color_mode": "single", "options": {"A": {"axis": "x", "angle": 150, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 60, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "z", "angle": 30, "direction": "clockwise", "filename": "choice2.png"}, "D": {"axis": "y", "angle": 120, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "C", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 30\u00b0 clockwise around the Z axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.6847382365474122, 0.05091185195124337, 0.4519625762476858], [0.6847382365474122, 0.05091185195124337, 0.4519625762476858], [0.6847382365474122, 0.05091185195124337, 0.4519625762476858], [0.6847382365474122, 0.05091185195124337, 0.4519625762476858], [0.6847382365474122, 0.05091185195124337, 0.4519625762476858], [0.6847382365474122, 0.05091185195124337, 0.4519625762476858], [0.48601385949817166, 0, 0.5131171755413199], [0.48601385949817166, 0, 0.5131171755413199], [0.48601385949817166, 0, 0.5131171755413199], [0.48601385949817166, 0, 0.5131171755413199], [0.48601385949817166, 0, 0.5131171755413199], [0.48601385949817166, 0, 0.5131171755413199], [0.4623950491784128, 0.14439713048602493, 0.6566184375132529], [0.4623950491784128, 0.14439713048602493, 0.6566184375132529], [0.4623950491784128, 0.14439713048602493, 0.6566184375132529], [0.4623950491784128, 0.14439713048602493, 0.6566184375132529], [0.4623950491784128, 0.14439713048602493, 0.6566184375132529], [0.4623950491784128, 0.14439713048602493, 0.6566184375132529], [0.6344046124203531, 0.15096158283864816, 0.5819191370024137], [0.6344046124203531, 0.15096158283864816, 0.5819191370024137], [0.6344046124203531, 0.15096158283864816, 0.5819191370024137], [0.6344046124203531, 0.15096158283864816, 0.5819191370024137], [0.6344046124203531, 0.15096158283864816, 0.5819191370024137], [0.6344046124203531, 0.15096158283864816, 0.5819191370024137]]}

medium_0001

A

medium

{"question_id": "medium_0001", "num_cubes": 3, "difficulty": "medium", "rotation_task": {"axis": "y", "angle": 60, "direction": "clockwise"}, "color_mode": "single", "options": {"A": {"axis": "y", "angle": 60, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "x", "angle": 90, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "z", "angle": 120, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "z", "angle": 150, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "A", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 60\u00b0 clockwise around the Y axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.35281856646637866, 0.8027392034702424, 0.43954374999126694], [0.35281856646637866, 0.8027392034702424, 0.43954374999126694], [0.35281856646637866, 0.8027392034702424, 0.43954374999126694], [0.35281856646637866, 0.8027392034702424, 0.43954374999126694], [0.35281856646637866, 0.8027392034702424, 0.43954374999126694], [0.35281856646637866, 0.8027392034702424, 0.43954374999126694], [0.15291624413997895, 0.9673761805268621, 0.594659591539674], [0.15291624413997895, 0.9673761805268621, 0.594659591539674], [0.15291624413997895, 0.9673761805268621, 0.594659591539674], [0.15291624413997895, 0.9673761805268621, 0.594659591539674], [0.15291624413997895, 0.9673761805268621, 0.594659591539674], [0.15291624413997895, 0.9673761805268621, 0.594659591539674], [0.08030825855574183, 0.8700286326443225, 0.5878208222714897], [0.08030825855574183, 0.8700286326443225, 0.5878208222714897], [0.08030825855574183, 0.8700286326443225, 0.5878208222714897], [0.08030825855574183, 0.8700286326443225, 0.5878208222714897], [0.08030825855574183, 0.8700286326443225, 0.5878208222714897], [0.08030825855574183, 0.8700286326443225, 0.5878208222714897]]}

medium_0002

D

medium

{"question_id": "medium_0002", "num_cubes": 4, "difficulty": "medium", "rotation_task": {"axis": "z", "angle": 60, "direction": "counter-clockwise"}, "color_mode": "single", "options": {"A": {"axis": "x", "angle": 120, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 150, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 30, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "z", "angle": 60, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "D", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 60\u00b0 counter-clockwise around the Z axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.34355573463756717, 0.980759965415012, 0.5871862075614291], [0.34355573463756717, 0.980759965415012, 0.5871862075614291], [0.34355573463756717, 0.980759965415012, 0.5871862075614291], [0.34355573463756717, 0.980759965415012, 0.5871862075614291], [0.34355573463756717, 0.980759965415012, 0.5871862075614291], [0.34355573463756717, 0.980759965415012, 0.5871862075614291], [0.471820494788141, 1, 0.49637629748694645], [0.471820494788141, 1, 0.49637629748694645], [0.471820494788141, 1, 0.49637629748694645], [0.471820494788141, 1, 0.49637629748694645], [0.471820494788141, 1, 0.49637629748694645], [0.471820494788141, 1, 0.49637629748694645], [0.5350532300322128, 1, 0.41511789732208537], [0.5350532300322128, 1, 0.41511789732208537], [0.5350532300322128, 1, 0.41511789732208537], [0.5350532300322128, 1, 0.41511789732208537], [0.5350532300322128, 1, 0.41511789732208537], [0.5350532300322128, 1, 0.41511789732208537], [0.4630535910576864, 1, 0.520631740174498], [0.4630535910576864, 1, 0.520631740174498], [0.4630535910576864, 1, 0.520631740174498], [0.4630535910576864, 1, 0.520631740174498], [0.4630535910576864, 1, 0.520631740174498], [0.4630535910576864, 1, 0.520631740174498]]}

medium_0003

C

medium

{"question_id": "medium_0003", "num_cubes": 3, "difficulty": "medium", "rotation_task": {"axis": "z", "angle": 120, "direction": "counter-clockwise"}, "color_mode": "single", "options": {"A": {"axis": "x", "angle": 180, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 120, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "z", "angle": 120, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "y", "angle": 60, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "C", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 120\u00b0 counter-clockwise around the Z axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.6930442687433215, 0.38925315811778977, 0.801548801972023], [0.6930442687433215, 0.38925315811778977, 0.801548801972023], [0.6930442687433215, 0.38925315811778977, 0.801548801972023], [0.6930442687433215, 0.38925315811778977, 0.801548801972023], [0.6930442687433215, 0.38925315811778977, 0.801548801972023], [0.6930442687433215, 0.38925315811778977, 0.801548801972023], [0.8143873240855707, 0.45939917344921966, 0.9359628879902494], [0.8143873240855707, 0.45939917344921966, 0.9359628879902494], [0.8143873240855707, 0.45939917344921966, 0.9359628879902494], [0.8143873240855707, 0.45939917344921966, 0.9359628879902494], [0.8143873240855707, 0.45939917344921966, 0.9359628879902494], [0.8143873240855707, 0.45939917344921966, 0.9359628879902494], [0.926439301835323, 0.46896428665128304, 1], [0.926439301835323, 0.46896428665128304, 1], [0.926439301835323, 0.46896428665128304, 1], [0.926439301835323, 0.46896428665128304, 1], [0.926439301835323, 0.46896428665128304, 1], [0.926439301835323, 0.46896428665128304, 1]]}

medium_0004

D

medium

{"question_id": "medium_0004", "num_cubes": 4, "difficulty": "medium", "rotation_task": {"axis": "y", "angle": 150, "direction": "counter-clockwise"}, "color_mode": "single", "options": {"A": {"axis": "x", "angle": 180, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "z", "angle": 30, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 150, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "y", "angle": 150, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "D", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 150\u00b0 counter-clockwise around the Y axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.21966639009860328, 0.9461348031724297, 0.10546639426529586], [0.21966639009860328, 0.9461348031724297, 0.10546639426529586], [0.21966639009860328, 0.9461348031724297, 0.10546639426529586], [0.21966639009860328, 0.9461348031724297, 0.10546639426529586], [0.21966639009860328, 0.9461348031724297, 0.10546639426529586], [0.21966639009860328, 0.9461348031724297, 0.10546639426529586], [0.32192372593598123, 0.7602191377988933, 0], [0.32192372593598123, 0.7602191377988933, 0], [0.32192372593598123, 0.7602191377988933, 0], [0.32192372593598123, 0.7602191377988933, 0], [0.32192372593598123, 0.7602191377988933, 0], [0.32192372593598123, 0.7602191377988933, 0]]}

medium_0005

A

medium

{"question_id": "medium_0005", "num_cubes": 2, "difficulty": "medium", "rotation_task": {"axis": "x", "angle": 90, "direction": "clockwise"}, "color_mode": "single", "options": {"A": {"axis": "x", "angle": 90, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 30, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "y", "angle": 60, "direction": "clockwise", "filename": "choice2.png"}, "D": {"axis": "y", "angle": 120, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "A", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 90\u00b0 clockwise around the X axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.6214342442492535, 0.36357849221760175, 0.9523565267861904], [0.6214342442492535, 0.36357849221760175, 0.9523565267861904], [0.6214342442492535, 0.36357849221760175, 0.9523565267861904], [0.6214342442492535, 0.36357849221760175, 0.9523565267861904], [0.6214342442492535, 0.36357849221760175, 0.9523565267861904], [0.6214342442492535, 0.36357849221760175, 0.9523565267861904], [0.5538199667588228, 0.5138196858204387, 1], [0.5538199667588228, 0.5138196858204387, 1], [0.5538199667588228, 0.5138196858204387, 1], [0.5538199667588228, 0.5138196858204387, 1], [0.5538199667588228, 0.5138196858204387, 1], [0.5538199667588228, 0.5138196858204387, 1]]}

medium_0006

C

medium

{"question_id": "medium_0006", "num_cubes": 3, "difficulty": "medium", "rotation_task": {"axis": "y", "angle": 90, "direction": "clockwise"}, "color_mode": "single", "options": {"A": {"axis": "y", "angle": 150, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "z", "angle": 30, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "y", "angle": 90, "direction": "clockwise", "filename": "choice2.png"}, "D": {"axis": "z", "angle": 180, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "C", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 90\u00b0 clockwise around the Y axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.48740880904710154, 0.768438061516112, 0.16609044739468984], [0.48740880904710154, 0.768438061516112, 0.16609044739468984], [0.48740880904710154, 0.768438061516112, 0.16609044739468984], [0.48740880904710154, 0.768438061516112, 0.16609044739468984], [0.48740880904710154, 0.768438061516112, 0.16609044739468984], [0.48740880904710154, 0.768438061516112, 0.16609044739468984], [0.4197231118402168, 0.7171201689858432, 0.32221192951403455], [0.4197231118402168, 0.7171201689858432, 0.32221192951403455], [0.4197231118402168, 0.7171201689858432, 0.32221192951403455], [0.4197231118402168, 0.7171201689858432, 0.32221192951403455], [0.4197231118402168, 0.7171201689858432, 0.32221192951403455], [0.4197231118402168, 0.7171201689858432, 0.32221192951403455], [0.3276603016969104, 0.7979525310988116, 0.4911737226013276], [0.3276603016969104, 0.7979525310988116, 0.4911737226013276], [0.3276603016969104, 0.7979525310988116, 0.4911737226013276], [0.3276603016969104, 0.7979525310988116, 0.4911737226013276], [0.3276603016969104, 0.7979525310988116, 0.4911737226013276], [0.3276603016969104, 0.7979525310988116, 0.4911737226013276]]}

medium_0007

C

medium

{"question_id": "medium_0007", "num_cubes": 3, "difficulty": "medium", "rotation_task": {"axis": "y", "angle": 120, "direction": "counter-clockwise"}, "color_mode": "single", "options": {"A": {"axis": "z", "angle": 180, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "z", "angle": 30, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "y", "angle": 120, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "z", "angle": 60, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "C", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 120\u00b0 counter-clockwise around the Y axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.9622397241857565, 0.5661469486923287, 0.8259951045912324], [0.9622397241857565, 0.5661469486923287, 0.8259951045912324], [0.9622397241857565, 0.5661469486923287, 0.8259951045912324], [0.9622397241857565, 0.5661469486923287, 0.8259951045912324], [0.9622397241857565, 0.5661469486923287, 0.8259951045912324], [0.9622397241857565, 0.5661469486923287, 0.8259951045912324], [0.845298606406364, 0.4403730650105623, 0.6390252394578468], [0.845298606406364, 0.4403730650105623, 0.6390252394578468], [0.845298606406364, 0.4403730650105623, 0.6390252394578468], [0.845298606406364, 0.4403730650105623, 0.6390252394578468], [0.845298606406364, 0.4403730650105623, 0.6390252394578468], [0.845298606406364, 0.4403730650105623, 0.6390252394578468], [0.7007187832240548, 0.24309514106567082, 0.7951842078218669], [0.7007187832240548, 0.24309514106567082, 0.7951842078218669], [0.7007187832240548, 0.24309514106567082, 0.7951842078218669], [0.7007187832240548, 0.24309514106567082, 0.7951842078218669], [0.7007187832240548, 0.24309514106567082, 0.7951842078218669], [0.7007187832240548, 0.24309514106567082, 0.7951842078218669]]}

medium_0008

B

medium

{"question_id": "medium_0008", "num_cubes": 2, "difficulty": "medium", "rotation_task": {"axis": "x", "angle": 150, "direction": "counter-clockwise"}, "color_mode": "single", "options": {"A": {"axis": "y", "angle": 150, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "x", "angle": 150, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "y", "angle": 60, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "y", "angle": 150, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "B", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 150\u00b0 counter-clockwise around the X axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0, 0.7182821347981336, 0.0893125295638642], [0, 0.7182821347981336, 0.0893125295638642], [0, 0.7182821347981336, 0.0893125295638642], [0, 0.7182821347981336, 0.0893125295638642], [0, 0.7182821347981336, 0.0893125295638642], [0, 0.7182821347981336, 0.0893125295638642], [0.18390954302478252, 0.5370171973486548, 0.17959622498389843], [0.18390954302478252, 0.5370171973486548, 0.17959622498389843], [0.18390954302478252, 0.5370171973486548, 0.17959622498389843], [0.18390954302478252, 0.5370171973486548, 0.17959622498389843], [0.18390954302478252, 0.5370171973486548, 0.17959622498389843], [0.18390954302478252, 0.5370171973486548, 0.17959622498389843]]}

medium_0009

A

medium

{"question_id": "medium_0009", "num_cubes": 2, "difficulty": "medium", "rotation_task": {"axis": "y", "angle": 90, "direction": "counter-clockwise"}, "color_mode": "single", "options": {"A": {"axis": "y", "angle": 90, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "z", "angle": 30, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "y", "angle": 30, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "z", "angle": 90, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "A", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 90\u00b0 counter-clockwise around the Y axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.7990893605625391, 0.49027229027806746, 0.17667148894638474], [0.7990893605625391, 0.49027229027806746, 0.17667148894638474], [0.7990893605625391, 0.49027229027806746, 0.17667148894638474], [0.7990893605625391, 0.49027229027806746, 0.17667148894638474], [0.7990893605625391, 0.49027229027806746, 0.17667148894638474], [0.7990893605625391, 0.49027229027806746, 0.17667148894638474], [0.6086351897721621, 0.2972870102379147, 0.11957252168250226], [0.6086351897721621, 0.2972870102379147, 0.11957252168250226], [0.6086351897721621, 0.2972870102379147, 0.11957252168250226], [0.6086351897721621, 0.2972870102379147, 0.11957252168250226], [0.6086351897721621, 0.2972870102379147, 0.11957252168250226], [0.6086351897721621, 0.2972870102379147, 0.11957252168250226]]}

medium_0010

A

medium

{"question_id": "medium_0010", "num_cubes": 3, "difficulty": "medium", "rotation_task": {"axis": "y", "angle": 180, "direction": "counter-clockwise"}, "color_mode": "single", "options": {"A": {"axis": "y", "angle": 180, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "z", "angle": 60, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 150, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "z", "angle": 30, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "A", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 180\u00b0 counter-clockwise around the Y axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[1, 0.09732239874496565, 0.3812186857913455], [1, 0.09732239874496565, 0.3812186857913455], [1, 0.09732239874496565, 0.3812186857913455], [1, 0.09732239874496565, 0.3812186857913455], [1, 0.09732239874496565, 0.3812186857913455], [1, 0.09732239874496565, 0.3812186857913455], [1, 0.08148632672418266, 0.2111237734644022], [1, 0.08148632672418266, 0.2111237734644022], [1, 0.08148632672418266, 0.2111237734644022], [1, 0.08148632672418266, 0.2111237734644022], [1, 0.08148632672418266, 0.2111237734644022], [1, 0.08148632672418266, 0.2111237734644022], [0.8481016682351703, 0.28117272099661805, 0.16996666594320775], [0.8481016682351703, 0.28117272099661805, 0.16996666594320775], [0.8481016682351703, 0.28117272099661805, 0.16996666594320775], [0.8481016682351703, 0.28117272099661805, 0.16996666594320775], [0.8481016682351703, 0.28117272099661805, 0.16996666594320775], [0.8481016682351703, 0.28117272099661805, 0.16996666594320775]]}

medium_0011

B

medium

{"question_id": "medium_0011", "num_cubes": 4, "difficulty": "medium", "rotation_task": {"axis": "z", "angle": 120, "direction": "clockwise"}, "color_mode": "single", "options": {"A": {"axis": "x", "angle": 60, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "z", "angle": 120, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "z", "angle": 30, "direction": "clockwise", "filename": "choice2.png"}, "D": {"axis": "y", "angle": 150, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "B", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 120\u00b0 clockwise around the Z axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.865027382500261, 0.3422509755286215, 0.5000154702574062], [0.865027382500261, 0.3422509755286215, 0.5000154702574062], [0.865027382500261, 0.3422509755286215, 0.5000154702574062], [0.865027382500261, 0.3422509755286215, 0.5000154702574062], [0.865027382500261, 0.3422509755286215, 0.5000154702574062], [0.865027382500261, 0.3422509755286215, 0.5000154702574062], [0.9311212053417915, 0.3612638669651511, 0.4808272828600467], [0.9311212053417915, 0.3612638669651511, 0.4808272828600467], [0.9311212053417915, 0.3612638669651511, 0.4808272828600467], [0.9311212053417915, 0.3612638669651511, 0.4808272828600467], [0.9311212053417915, 0.3612638669651511, 0.4808272828600467], [0.9311212053417915, 0.3612638669651511, 0.4808272828600467], [1, 0.5271234404585186, 0.6092757096134309], [1, 0.5271234404585186, 0.6092757096134309], [1, 0.5271234404585186, 0.6092757096134309], [1, 0.5271234404585186, 0.6092757096134309], [1, 0.5271234404585186, 0.6092757096134309], [1, 0.5271234404585186, 0.6092757096134309], [1, 0.39040023229282456, 0.517058991282636], [1, 0.39040023229282456, 0.517058991282636], [1, 0.39040023229282456, 0.517058991282636], [1, 0.39040023229282456, 0.517058991282636], [1, 0.39040023229282456, 0.517058991282636], [1, 0.39040023229282456, 0.517058991282636]]}

medium_0012

D

medium

{"question_id": "medium_0012", "num_cubes": 4, "difficulty": "medium", "rotation_task": {"axis": "y", "angle": 60, "direction": "clockwise"}, "color_mode": "single", "options": {"A": {"axis": "z", "angle": 180, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "x", "angle": 90, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 90, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "y", "angle": 60, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "D", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 60\u00b0 clockwise around the Y axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.7615782208851745, 0.8127483995599936, 0.04699753753226463], [0.7615782208851745, 0.8127483995599936, 0.04699753753226463], [0.7615782208851745, 0.8127483995599936, 0.04699753753226463], [0.7615782208851745, 0.8127483995599936, 0.04699753753226463], [0.7615782208851745, 0.8127483995599936, 0.04699753753226463], [0.7615782208851745, 0.8127483995599936, 0.04699753753226463], [0.92061900733636, 0.7689207946535013, 0], [0.92061900733636, 0.7689207946535013, 0], [0.92061900733636, 0.7689207946535013, 0], [0.92061900733636, 0.7689207946535013, 0], [0.92061900733636, 0.7689207946535013, 0], [0.92061900733636, 0.7689207946535013, 0], [0.7754697089728374, 0.9156763644621795, 0.0990984479083003], [0.7754697089728374, 0.9156763644621795, 0.0990984479083003], [0.7754697089728374, 0.9156763644621795, 0.0990984479083003], [0.7754697089728374, 0.9156763644621795, 0.0990984479083003], [0.7754697089728374, 0.9156763644621795, 0.0990984479083003], [0.7754697089728374, 0.9156763644621795, 0.0990984479083003]]}

medium_0013

A

medium

{"question_id": "medium_0013", "num_cubes": 4, "difficulty": "medium", "rotation_task": {"axis": "x", "angle": 90, "direction": "clockwise"}, "color_mode": "single", "options": {"A": {"axis": "x", "angle": 90, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 60, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "y", "angle": 90, "direction": "clockwise", "filename": "choice2.png"}, "D": {"axis": "x", "angle": 60, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "A", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 90\u00b0 clockwise around the X axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[1, 0.23963845137363476, 0.7816858151833757], [1, 0.23963845137363476, 0.7816858151833757], [1, 0.23963845137363476, 0.7816858151833757], [1, 0.23963845137363476, 0.7816858151833757], [1, 0.23963845137363476, 0.7816858151833757], [1, 0.23963845137363476, 0.7816858151833757], [1, 0.27742633129118965, 0.6075590460263443], [1, 0.27742633129118965, 0.6075590460263443], [1, 0.27742633129118965, 0.6075590460263443], [1, 0.27742633129118965, 0.6075590460263443], [1, 0.27742633129118965, 0.6075590460263443], [1, 0.27742633129118965, 0.6075590460263443], [1, 0.24376409338429278, 0.5767430553349318], [1, 0.24376409338429278, 0.5767430553349318], [1, 0.24376409338429278, 0.5767430553349318], [1, 0.24376409338429278, 0.5767430553349318], [1, 0.24376409338429278, 0.5767430553349318], [1, 0.24376409338429278, 0.5767430553349318], [0.982558017602128, 0.2302792509982362, 0.689481105583837], [0.982558017602128, 0.2302792509982362, 0.689481105583837], [0.982558017602128, 0.2302792509982362, 0.689481105583837], [0.982558017602128, 0.2302792509982362, 0.689481105583837], [0.982558017602128, 0.2302792509982362, 0.689481105583837], [0.982558017602128, 0.2302792509982362, 0.689481105583837]]}

medium_0014

C

medium

{"question_id": "medium_0014", "num_cubes": 2, "difficulty": "medium", "rotation_task": {"axis": "x", "angle": 180, "direction": "clockwise"}, "color_mode": "single", "options": {"A": {"axis": "x", "angle": 60, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "z", "angle": 150, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 180, "direction": "clockwise", "filename": "choice2.png"}, "D": {"axis": "y", "angle": 90, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "C", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 180\u00b0 clockwise around the X axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.8781094977222218, 0.31262725725501406, 0.4914139865876695], [0.8781094977222218, 0.31262725725501406, 0.4914139865876695], [0.8781094977222218, 0.31262725725501406, 0.4914139865876695], [0.8781094977222218, 0.31262725725501406, 0.4914139865876695], [0.8781094977222218, 0.31262725725501406, 0.4914139865876695], [0.8781094977222218, 0.31262725725501406, 0.4914139865876695], [1, 0.18723043458365396, 0.5805480432342035], [1, 0.18723043458365396, 0.5805480432342035], [1, 0.18723043458365396, 0.5805480432342035], [1, 0.18723043458365396, 0.5805480432342035], [1, 0.18723043458365396, 0.5805480432342035], [1, 0.18723043458365396, 0.5805480432342035]]}

medium_0015

D

medium

{"question_id": "medium_0015", "num_cubes": 2, "difficulty": "medium", "rotation_task": {"axis": "x", "angle": 180, "direction": "clockwise"}, "color_mode": "single", "options": {"A": {"axis": "x", "angle": 120, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 150, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 90, "direction": "clockwise", "filename": "choice2.png"}, "D": {"axis": "x", "angle": 180, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "D", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 180\u00b0 clockwise around the X axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.16838015139132978, 0.3089553485503903, 0.8702994140185192], [0.16838015139132978, 0.3089553485503903, 0.8702994140185192], [0.16838015139132978, 0.3089553485503903, 0.8702994140185192], [0.16838015139132978, 0.3089553485503903, 0.8702994140185192], [0.16838015139132978, 0.3089553485503903, 0.8702994140185192], [0.16838015139132978, 0.3089553485503903, 0.8702994140185192], [0.11527159716124832, 0.371648389927338, 0.6735670085837422], [0.11527159716124832, 0.371648389927338, 0.6735670085837422], [0.11527159716124832, 0.371648389927338, 0.6735670085837422], [0.11527159716124832, 0.371648389927338, 0.6735670085837422], [0.11527159716124832, 0.371648389927338, 0.6735670085837422], [0.11527159716124832, 0.371648389927338, 0.6735670085837422]]}

medium_0016

C

medium

{"question_id": "medium_0016", "num_cubes": 3, "difficulty": "medium", "rotation_task": {"axis": "y", "angle": 150, "direction": "counter-clockwise"}, "color_mode": "single", "options": {"A": {"axis": "y", "angle": 30, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "x", "angle": 30, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "y", "angle": 150, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "x", "angle": 150, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "C", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 150\u00b0 counter-clockwise around the Y axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.26813031551189004, 0.853464959771148, 0], [0.26813031551189004, 0.853464959771148, 0], [0.26813031551189004, 0.853464959771148, 0], [0.26813031551189004, 0.853464959771148, 0], [0.26813031551189004, 0.853464959771148, 0], [0.26813031551189004, 0.853464959771148, 0], [0.17479215353332217, 1, 0], [0.17479215353332217, 1, 0], [0.17479215353332217, 1, 0], [0.17479215353332217, 1, 0], [0.17479215353332217, 1, 0], [0.17479215353332217, 1, 0], [0.12638679077395443, 1, 0], [0.12638679077395443, 1, 0], [0.12638679077395443, 1, 0], [0.12638679077395443, 1, 0], [0.12638679077395443, 1, 0], [0.12638679077395443, 1, 0]]}

medium_0017

B

medium

{"question_id": "medium_0017", "num_cubes": 4, "difficulty": "medium", "rotation_task": {"axis": "y", "angle": 120, "direction": "clockwise"}, "color_mode": "single", "options": {"A": {"axis": "y", "angle": 180, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 120, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 60, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "x", "angle": 90, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "B", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 120\u00b0 clockwise around the Y axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0, 1, 0.10344543642973889], [0, 1, 0.10344543642973889], [0, 1, 0.10344543642973889], [0, 1, 0.10344543642973889], [0, 1, 0.10344543642973889], [0, 1, 0.10344543642973889], [0, 0.9593707368451082, 0.029669379731903506], [0, 0.9593707368451082, 0.029669379731903506], [0, 0.9593707368451082, 0.029669379731903506], [0, 0.9593707368451082, 0.029669379731903506], [0, 0.9593707368451082, 0.029669379731903506], [0, 0.9593707368451082, 0.029669379731903506], [0, 0.9792922950632083, 0.21417629062420354], [0, 0.9792922950632083, 0.21417629062420354], [0, 0.9792922950632083, 0.21417629062420354], [0, 0.9792922950632083, 0.21417629062420354], [0, 0.9792922950632083, 0.21417629062420354], [0, 0.9792922950632083, 0.21417629062420354], [0, 0.970239829778134, 0.36429258698406375], [0, 0.970239829778134, 0.36429258698406375], [0, 0.970239829778134, 0.36429258698406375], [0, 0.970239829778134, 0.36429258698406375], [0, 0.970239829778134, 0.36429258698406375], [0, 0.970239829778134, 0.36429258698406375]]}

medium_0018

A

medium

{"question_id": "medium_0018", "num_cubes": 2, "difficulty": "medium", "rotation_task": {"axis": "z", "angle": 150, "direction": "counter-clockwise"}, "color_mode": "single", "options": {"A": {"axis": "z", "angle": 150, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "x", "angle": 30, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "z", "angle": 60, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "x", "angle": 60, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "A", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 150\u00b0 counter-clockwise around the Z axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.11119114957139181, 0.993930734125283, 0.31860115893143115], [0.11119114957139181, 0.993930734125283, 0.31860115893143115], [0.11119114957139181, 0.993930734125283, 0.31860115893143115], [0.11119114957139181, 0.993930734125283, 0.31860115893143115], [0.11119114957139181, 0.993930734125283, 0.31860115893143115], [0.11119114957139181, 0.993930734125283, 0.31860115893143115], [0.278257208303477, 0.9777592105467688, 0.36794607983061844], [0.278257208303477, 0.9777592105467688, 0.36794607983061844], [0.278257208303477, 0.9777592105467688, 0.36794607983061844], [0.278257208303477, 0.9777592105467688, 0.36794607983061844], [0.278257208303477, 0.9777592105467688, 0.36794607983061844], [0.278257208303477, 0.9777592105467688, 0.36794607983061844]]}

medium_0019

C

medium

{"question_id": "medium_0019", "num_cubes": 2, "difficulty": "medium", "rotation_task": {"axis": "z", "angle": 30, "direction": "clockwise"}, "color_mode": "single", "options": {"A": {"axis": "y", "angle": 120, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "x", "angle": 30, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "z", "angle": 30, "direction": "clockwise", "filename": "choice2.png"}, "D": {"axis": "x", "angle": 60, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "C", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 30\u00b0 clockwise around the Z axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.7522534961789458, 0.25573602463941497, 0.9862265885041123], [0.7522534961789458, 0.25573602463941497, 0.9862265885041123], [0.7522534961789458, 0.25573602463941497, 0.9862265885041123], [0.7522534961789458, 0.25573602463941497, 0.9862265885041123], [0.7522534961789458, 0.25573602463941497, 0.9862265885041123], [0.7522534961789458, 0.25573602463941497, 0.9862265885041123], [0.7141040499231112, 0.23325222815742488, 0.8502324560000065], [0.7141040499231112, 0.23325222815742488, 0.8502324560000065], [0.7141040499231112, 0.23325222815742488, 0.8502324560000065], [0.7141040499231112, 0.23325222815742488, 0.8502324560000065], [0.7141040499231112, 0.23325222815742488, 0.8502324560000065], [0.7141040499231112, 0.23325222815742488, 0.8502324560000065]]}

hard_0000

D

hard

{"question_id": "hard_0000", "num_cubes": 6, "difficulty": "hard", "rotation_task": {"axis": "z", "angle": 60, "direction": "clockwise"}, "color_mode": "single", "options": {"A": {"axis": "x", "angle": 150, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "z", "angle": 90, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "y", "angle": 180, "direction": "clockwise", "filename": "choice2.png"}, "D": {"axis": "z", "angle": 60, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "D", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 60\u00b0 clockwise around the Z axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.840214762040254, 0.4911659085897371, 0.8153064111142033], [0.840214762040254, 0.4911659085897371, 0.8153064111142033], [0.840214762040254, 0.4911659085897371, 0.8153064111142033], [0.840214762040254, 0.4911659085897371, 0.8153064111142033], [0.840214762040254, 0.4911659085897371, 0.8153064111142033], [0.840214762040254, 0.4911659085897371, 0.8153064111142033], [0.8960114606062088, 0.5350967342065698, 0.9169564633528867], [0.8960114606062088, 0.5350967342065698, 0.9169564633528867], [0.8960114606062088, 0.5350967342065698, 0.9169564633528867], [0.8960114606062088, 0.5350967342065698, 0.9169564633528867], [0.8960114606062088, 0.5350967342065698, 0.9169564633528867], [0.8960114606062088, 0.5350967342065698, 0.9169564633528867], [1, 0.5771474994244687, 0.9438409361023501], [1, 0.5771474994244687, 0.9438409361023501], [1, 0.5771474994244687, 0.9438409361023501], [1, 0.5771474994244687, 0.9438409361023501], [1, 0.5771474994244687, 0.9438409361023501], [1, 0.5771474994244687, 0.9438409361023501], [1, 0.5029268271764407, 0.7922044360204439], [1, 0.5029268271764407, 0.7922044360204439], [1, 0.5029268271764407, 0.7922044360204439], [1, 0.5029268271764407, 0.7922044360204439], [1, 0.5029268271764407, 0.7922044360204439], [1, 0.5029268271764407, 0.7922044360204439], [0.8672825711973474, 0.6534670988538553, 0.8105431345693972], [0.8672825711973474, 0.6534670988538553, 0.8105431345693972], [0.8672825711973474, 0.6534670988538553, 0.8105431345693972], [0.8672825711973474, 0.6534670988538553, 0.8105431345693972], [0.8672825711973474, 0.6534670988538553, 0.8105431345693972], [0.8672825711973474, 0.6534670988538553, 0.8105431345693972], [0.722058811767146, 0.8176625158909226, 0.8635652396697057], [0.722058811767146, 0.8176625158909226, 0.8635652396697057], [0.722058811767146, 0.8176625158909226, 0.8635652396697057], [0.722058811767146, 0.8176625158909226, 0.8635652396697057], [0.722058811767146, 0.8176625158909226, 0.8635652396697057], [0.722058811767146, 0.8176625158909226, 0.8635652396697057]]}

hard_0001

D

hard

{"question_id": "hard_0001", "num_cubes": 8, "difficulty": "hard", "rotation_task": {"axis": "y", "angle": 90, "direction": "clockwise"}, "color_mode": "single", "options": {"A": {"axis": "y", "angle": 180, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "z", "angle": 30, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "z", "angle": 60, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "y", "angle": 90, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "D", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 90\u00b0 clockwise around the Y axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.19136823142159276, 0.6076264215798107, 0.8176416227377893], [0.19136823142159276, 0.6076264215798107, 0.8176416227377893], [0.19136823142159276, 0.6076264215798107, 0.8176416227377893], [0.19136823142159276, 0.6076264215798107, 0.8176416227377893], [0.19136823142159276, 0.6076264215798107, 0.8176416227377893], [0.19136823142159276, 0.6076264215798107, 0.8176416227377893], [0.20717399199638148, 0.4958892649692962, 0.7878117374230484], [0.20717399199638148, 0.4958892649692962, 0.7878117374230484], [0.20717399199638148, 0.4958892649692962, 0.7878117374230484], [0.20717399199638148, 0.4958892649692962, 0.7878117374230484], [0.20717399199638148, 0.4958892649692962, 0.7878117374230484], [0.20717399199638148, 0.4958892649692962, 0.7878117374230484], [0.401261714234889, 0.32529248516159065, 0.7949179669980284], [0.401261714234889, 0.32529248516159065, 0.7949179669980284], [0.401261714234889, 0.32529248516159065, 0.7949179669980284], [0.401261714234889, 0.32529248516159065, 0.7949179669980284], [0.401261714234889, 0.32529248516159065, 0.7949179669980284], [0.401261714234889, 0.32529248516159065, 0.7949179669980284], [0.4953473256141733, 0.3006026201439007, 0.7684432061914626], [0.4953473256141733, 0.3006026201439007, 0.7684432061914626], [0.4953473256141733, 0.3006026201439007, 0.7684432061914626], [0.4953473256141733, 0.3006026201439007, 0.7684432061914626], [0.4953473256141733, 0.3006026201439007, 0.7684432061914626], [0.4953473256141733, 0.3006026201439007, 0.7684432061914626], [0.6364084437470823, 0.39540668622544545, 0.9646543676690804], [0.6364084437470823, 0.39540668622544545, 0.9646543676690804], [0.6364084437470823, 0.39540668622544545, 0.9646543676690804], [0.6364084437470823, 0.39540668622544545, 0.9646543676690804], [0.6364084437470823, 0.39540668622544545, 0.9646543676690804], [0.6364084437470823, 0.39540668622544545, 0.9646543676690804]]}

hard_0002

D

hard

{"question_id": "hard_0002", "num_cubes": 8, "difficulty": "hard", "rotation_task": {"axis": "y", "angle": 60, "direction": "counter-clockwise"}, "color_mode": "single", "options": {"A": {"axis": "z", "angle": 150, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "x", "angle": 60, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "z", "angle": 90, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "y", "angle": 60, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "D", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 60\u00b0 counter-clockwise around the Y axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[1, 0.5353053005670617, 1], [1, 0.5353053005670617, 1], [1, 0.5353053005670617, 1], [1, 0.5353053005670617, 1], [1, 0.5353053005670617, 1], [1, 0.5353053005670617, 1], [0.977706435126855, 0.3930737717395465, 0.8938271128102204], [0.977706435126855, 0.3930737717395465, 0.8938271128102204], [0.977706435126855, 0.3930737717395465, 0.8938271128102204], [0.977706435126855, 0.3930737717395465, 0.8938271128102204], [0.977706435126855, 0.3930737717395465, 0.8938271128102204], [0.977706435126855, 0.3930737717395465, 0.8938271128102204], [1, 0.3341368317193434, 0.9851697075386736], [1, 0.3341368317193434, 0.9851697075386736], [1, 0.3341368317193434, 0.9851697075386736], [1, 0.3341368317193434, 0.9851697075386736], [1, 0.3341368317193434, 0.9851697075386736], [1, 0.3341368317193434, 0.9851697075386736], [0.8502980788008885, 0.45897056852537915, 1], [0.8502980788008885, 0.45897056852537915, 1], [0.8502980788008885, 0.45897056852537915, 1], [0.8502980788008885, 0.45897056852537915, 1], [0.8502980788008885, 0.45897056852537915, 1], [0.8502980788008885, 0.45897056852537915, 1], [0.776051691987298, 0.5670024798864475, 1], [0.776051691987298, 0.5670024798864475, 1], [0.776051691987298, 0.5670024798864475, 1], [0.776051691987298, 0.5670024798864475, 1], [0.776051691987298, 0.5670024798864475, 1], [0.776051691987298, 0.5670024798864475, 1], [0.6696757726637719, 0.4097987506358691, 0.8028640904069684], [0.6696757726637719, 0.4097987506358691, 0.8028640904069684], [0.6696757726637719, 0.4097987506358691, 0.8028640904069684], [0.6696757726637719, 0.4097987506358691, 0.8028640904069684], [0.6696757726637719, 0.4097987506358691, 0.8028640904069684], [0.6696757726637719, 0.4097987506358691, 0.8028640904069684], [0.581827217871464, 0.3769682277463158, 0.6108872124886542], [0.581827217871464, 0.3769682277463158, 0.6108872124886542], [0.581827217871464, 0.3769682277463158, 0.6108872124886542], [0.581827217871464, 0.3769682277463158, 0.6108872124886542], [0.581827217871464, 0.3769682277463158, 0.6108872124886542], [0.581827217871464, 0.3769682277463158, 0.6108872124886542]]}

hard_0003

D

hard

{"question_id": "hard_0003", "num_cubes": 6, "difficulty": "hard", "rotation_task": {"axis": "x", "angle": 90, "direction": "counter-clockwise"}, "color_mode": "single", "options": {"A": {"axis": "x", "angle": 120, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "z", "angle": 60, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "y", "angle": 60, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "x", "angle": 90, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "D", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 90\u00b0 counter-clockwise around the X axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.44193942178220885, 1, 0.8077036687019378], [0.44193942178220885, 1, 0.8077036687019378], [0.44193942178220885, 1, 0.8077036687019378], [0.44193942178220885, 1, 0.8077036687019378], [0.44193942178220885, 1, 0.8077036687019378], [0.44193942178220885, 1, 0.8077036687019378], [0.33827895235687483, 0.9905139931269415, 0.660039916606359], [0.33827895235687483, 0.9905139931269415, 0.660039916606359], [0.33827895235687483, 0.9905139931269415, 0.660039916606359], [0.33827895235687483, 0.9905139931269415, 0.660039916606359], [0.33827895235687483, 0.9905139931269415, 0.660039916606359], [0.33827895235687483, 0.9905139931269415, 0.660039916606359], [0.23542634116057828, 0.9127968397856232, 0.5201695116286092], [0.23542634116057828, 0.9127968397856232, 0.5201695116286092], [0.23542634116057828, 0.9127968397856232, 0.5201695116286092], [0.23542634116057828, 0.9127968397856232, 0.5201695116286092], [0.23542634116057828, 0.9127968397856232, 0.5201695116286092], [0.23542634116057828, 0.9127968397856232, 0.5201695116286092], [0.08091570927019207, 0.9213124759191722, 0.6962151323984227], [0.08091570927019207, 0.9213124759191722, 0.6962151323984227], [0.08091570927019207, 0.9213124759191722, 0.6962151323984227], [0.08091570927019207, 0.9213124759191722, 0.6962151323984227], [0.08091570927019207, 0.9213124759191722, 0.6962151323984227], [0.08091570927019207, 0.9213124759191722, 0.6962151323984227]]}

hard_0004

A

hard

{"question_id": "hard_0004", "num_cubes": 8, "difficulty": "hard", "rotation_task": {"axis": "z", "angle": 30, "direction": "counter-clockwise"}, "color_mode": "single", "options": {"A": {"axis": "z", "angle": 30, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 150, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "y", "angle": 90, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "y", "angle": 150, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "A", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 30\u00b0 counter-clockwise around the Z axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.7328315669373593, 0, 0.2979861440863139], [0.7328315669373593, 0, 0.2979861440863139], [0.7328315669373593, 0, 0.2979861440863139], [0.7328315669373593, 0, 0.2979861440863139], [0.7328315669373593, 0, 0.2979861440863139], [0.7328315669373593, 0, 0.2979861440863139], [0.6033284113092852, 0.1864929321229688, 0.20150743839424848], [0.6033284113092852, 0.1864929321229688, 0.20150743839424848], [0.6033284113092852, 0.1864929321229688, 0.20150743839424848], [0.6033284113092852, 0.1864929321229688, 0.20150743839424848], [0.6033284113092852, 0.1864929321229688, 0.20150743839424848], [0.6033284113092852, 0.1864929321229688, 0.20150743839424848], [0.40708237974773676, 0.0326562266166589, 0.245140690294856], [0.40708237974773676, 0.0326562266166589, 0.245140690294856], [0.40708237974773676, 0.0326562266166589, 0.245140690294856], [0.40708237974773676, 0.0326562266166589, 0.245140690294856], [0.40708237974773676, 0.0326562266166589, 0.245140690294856], [0.40708237974773676, 0.0326562266166589, 0.245140690294856], [0.23691905090707732, 0.1757409988437169, 0.13621910371282236], [0.23691905090707732, 0.1757409988437169, 0.13621910371282236], [0.23691905090707732, 0.1757409988437169, 0.13621910371282236], [0.23691905090707732, 0.1757409988437169, 0.13621910371282236], [0.23691905090707732, 0.1757409988437169, 0.13621910371282236], [0.23691905090707732, 0.1757409988437169, 0.13621910371282236], [0.29564271280148147, 0.07503642402180817, 0.04672536782453218], [0.29564271280148147, 0.07503642402180817, 0.04672536782453218], [0.29564271280148147, 0.07503642402180817, 0.04672536782453218], [0.29564271280148147, 0.07503642402180817, 0.04672536782453218], [0.29564271280148147, 0.07503642402180817, 0.04672536782453218], [0.29564271280148147, 0.07503642402180817, 0.04672536782453218]]}

hard_0005

A

hard

{"question_id": "hard_0005", "num_cubes": 5, "difficulty": "hard", "rotation_task": {"axis": "x", "angle": 150, "direction": "clockwise"}, "color_mode": "single", "options": {"A": {"axis": "x", "angle": 150, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "x", "angle": 60, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "z", "angle": 30, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "z", "angle": 60, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "A", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 150\u00b0 clockwise around the X axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.8838904910790679, 0.653687429373795, 0.39241790529515325], [0.8838904910790679, 0.653687429373795, 0.39241790529515325], [0.8838904910790679, 0.653687429373795, 0.39241790529515325], [0.8838904910790679, 0.653687429373795, 0.39241790529515325], [0.8838904910790679, 0.653687429373795, 0.39241790529515325], [0.8838904910790679, 0.653687429373795, 0.39241790529515325], [0.9173308837249889, 0.7221984456003463, 0.463605907974146], [0.9173308837249889, 0.7221984456003463, 0.463605907974146], [0.9173308837249889, 0.7221984456003463, 0.463605907974146], [0.9173308837249889, 0.7221984456003463, 0.463605907974146], [0.9173308837249889, 0.7221984456003463, 0.463605907974146], [0.9173308837249889, 0.7221984456003463, 0.463605907974146], [0.9500642919136892, 0.6848731806464391, 0.585559947138478], [0.9500642919136892, 0.6848731806464391, 0.585559947138478], [0.9500642919136892, 0.6848731806464391, 0.585559947138478], [0.9500642919136892, 0.6848731806464391, 0.585559947138478], [0.9500642919136892, 0.6848731806464391, 0.585559947138478], [0.9500642919136892, 0.6848731806464391, 0.585559947138478], [1, 0.8106772814415162, 0.46811448618570745], [1, 0.8106772814415162, 0.46811448618570745], [1, 0.8106772814415162, 0.46811448618570745], [1, 0.8106772814415162, 0.46811448618570745], [1, 0.8106772814415162, 0.46811448618570745], [1, 0.8106772814415162, 0.46811448618570745], [0.994459397218277, 0.8244450466056984, 0.663411245137167], [0.994459397218277, 0.8244450466056984, 0.663411245137167], [0.994459397218277, 0.8244450466056984, 0.663411245137167], [0.994459397218277, 0.8244450466056984, 0.663411245137167], [0.994459397218277, 0.8244450466056984, 0.663411245137167], [0.994459397218277, 0.8244450466056984, 0.663411245137167]]}

hard_0006

A

hard

{"question_id": "hard_0006", "num_cubes": 8, "difficulty": "hard", "rotation_task": {"axis": "x", "angle": 180, "direction": "counter-clockwise"}, "color_mode": "single", "options": {"A": {"axis": "x", "angle": 180, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "z", "angle": 180, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 120, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "x", "angle": 90, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "A", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 180\u00b0 counter-clockwise around the X axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.06331795815187005, 1, 0.9978534086719764], [0.06331795815187005, 1, 0.9978534086719764], [0.06331795815187005, 1, 0.9978534086719764], [0.06331795815187005, 1, 0.9978534086719764], [0.06331795815187005, 1, 0.9978534086719764], [0.06331795815187005, 1, 0.9978534086719764], [0, 1, 0.9203298206502215], [0, 1, 0.9203298206502215], [0, 1, 0.9203298206502215], [0, 1, 0.9203298206502215], [0, 1, 0.9203298206502215], [0, 1, 0.9203298206502215], [0, 1, 1], [0, 1, 1], [0, 1, 1], [0, 1, 1], [0, 1, 1], [0, 1, 1], [0.16661913104832282, 0.9800413297951527, 0.89660388107562], [0.16661913104832282, 0.9800413297951527, 0.89660388107562], [0.16661913104832282, 0.9800413297951527, 0.89660388107562], [0.16661913104832282, 0.9800413297951527, 0.89660388107562], [0.16661913104832282, 0.9800413297951527, 0.89660388107562], [0.16661913104832282, 0.9800413297951527, 0.89660388107562], [0.0058354783677702915, 0.7953512289370621, 0.9857118774244149], [0.0058354783677702915, 0.7953512289370621, 0.9857118774244149], [0.0058354783677702915, 0.7953512289370621, 0.9857118774244149], [0.0058354783677702915, 0.7953512289370621, 0.9857118774244149], [0.0058354783677702915, 0.7953512289370621, 0.9857118774244149], [0.0058354783677702915, 0.7953512289370621, 0.9857118774244149], [0.006212543616992, 0.7398272939332406, 0.96788364863302], [0.006212543616992, 0.7398272939332406, 0.96788364863302], [0.006212543616992, 0.7398272939332406, 0.96788364863302], [0.006212543616992, 0.7398272939332406, 0.96788364863302], [0.006212543616992, 0.7398272939332406, 0.96788364863302], [0.006212543616992, 0.7398272939332406, 0.96788364863302]]}

hard_0007

A

hard

{"question_id": "hard_0007", "num_cubes": 7, "difficulty": "hard", "rotation_task": {"axis": "x", "angle": 90, "direction": "counter-clockwise"}, "color_mode": "single", "options": {"A": {"axis": "x", "angle": 90, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 60, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 60, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "z", "angle": 90, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "A", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 90\u00b0 counter-clockwise around the X axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[1, 0.36207673861001743, 0.6079826582880069], [1, 0.36207673861001743, 0.6079826582880069], [1, 0.36207673861001743, 0.6079826582880069], [1, 0.36207673861001743, 0.6079826582880069], [1, 0.36207673861001743, 0.6079826582880069], [1, 0.36207673861001743, 0.6079826582880069], [1, 0.25858027561758024, 0.5221467446149763], [1, 0.25858027561758024, 0.5221467446149763], [1, 0.25858027561758024, 0.5221467446149763], [1, 0.25858027561758024, 0.5221467446149763], [1, 0.25858027561758024, 0.5221467446149763], [1, 0.25858027561758024, 0.5221467446149763], [0.994207810000204, 0.07782942981421939, 0.48025822795601136], [0.994207810000204, 0.07782942981421939, 0.48025822795601136], [0.994207810000204, 0.07782942981421939, 0.48025822795601136], [0.994207810000204, 0.07782942981421939, 0.48025822795601136], [0.994207810000204, 0.07782942981421939, 0.48025822795601136], [0.994207810000204, 0.07782942981421939, 0.48025822795601136], [0.9481516615325378, 0.21346409146781328, 0.3098901541295361], [0.9481516615325378, 0.21346409146781328, 0.3098901541295361], [0.9481516615325378, 0.21346409146781328, 0.3098901541295361], [0.9481516615325378, 0.21346409146781328, 0.3098901541295361], [0.9481516615325378, 0.21346409146781328, 0.3098901541295361], [0.9481516615325378, 0.21346409146781328, 0.3098901541295361], [1, 0.16047571238645295, 0.3625833538991802], [1, 0.16047571238645295, 0.3625833538991802], [1, 0.16047571238645295, 0.3625833538991802], [1, 0.16047571238645295, 0.3625833538991802], [1, 0.16047571238645295, 0.3625833538991802], [1, 0.16047571238645295, 0.3625833538991802], [1, 0.2639665045325532, 0.5342250978420022], [1, 0.2639665045325532, 0.5342250978420022], [1, 0.2639665045325532, 0.5342250978420022], [1, 0.2639665045325532, 0.5342250978420022], [1, 0.2639665045325532, 0.5342250978420022], [1, 0.2639665045325532, 0.5342250978420022], [0.9912349977166288, 0.06542615564283805, 0.33915997621729954], [0.9912349977166288, 0.06542615564283805, 0.33915997621729954], [0.9912349977166288, 0.06542615564283805, 0.33915997621729954], [0.9912349977166288, 0.06542615564283805, 0.33915997621729954], [0.9912349977166288, 0.06542615564283805, 0.33915997621729954], [0.9912349977166288, 0.06542615564283805, 0.33915997621729954]]}

hard_0008

D

hard

{"question_id": "hard_0008", "num_cubes": 7, "difficulty": "hard", "rotation_task": {"axis": "x", "angle": 150, "direction": "clockwise"}, "color_mode": "single", "options": {"A": {"axis": "z", "angle": 60, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 30, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "y", "angle": 90, "direction": "clockwise", "filename": "choice2.png"}, "D": {"axis": "x", "angle": 150, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "D", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 150\u00b0 clockwise around the X axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[1, 0.28987120442578573, 0.3383193073414242], [1, 0.28987120442578573, 0.3383193073414242], [1, 0.28987120442578573, 0.3383193073414242], [1, 0.28987120442578573, 0.3383193073414242], [1, 0.28987120442578573, 0.3383193073414242], [1, 0.28987120442578573, 0.3383193073414242], [1, 0.16911585461373924, 0.1757380377217143], [1, 0.16911585461373924, 0.1757380377217143], [1, 0.16911585461373924, 0.1757380377217143], [1, 0.16911585461373924, 0.1757380377217143], [1, 0.16911585461373924, 0.1757380377217143], [1, 0.16911585461373924, 0.1757380377217143], [1, 0.11639968612780302, 0.21127259774319052], [1, 0.11639968612780302, 0.21127259774319052], [1, 0.11639968612780302, 0.21127259774319052], [1, 0.11639968612780302, 0.21127259774319052], [1, 0.11639968612780302, 0.21127259774319052], [1, 0.11639968612780302, 0.21127259774319052], [0.9717010151474865, 0.25637775632452176, 0.17264386781303148], [0.9717010151474865, 0.25637775632452176, 0.17264386781303148], [0.9717010151474865, 0.25637775632452176, 0.17264386781303148], [0.9717010151474865, 0.25637775632452176, 0.17264386781303148], [0.9717010151474865, 0.25637775632452176, 0.17264386781303148], [0.9717010151474865, 0.25637775632452176, 0.17264386781303148], [0.8872237497129272, 0.3334177369906603, 0.1247146594333022], [0.8872237497129272, 0.3334177369906603, 0.1247146594333022], [0.8872237497129272, 0.3334177369906603, 0.1247146594333022], [0.8872237497129272, 0.3334177369906603, 0.1247146594333022], [0.8872237497129272, 0.3334177369906603, 0.1247146594333022], [0.8872237497129272, 0.3334177369906603, 0.1247146594333022], [0.7948348474998488, 0.24213590791713657, 0.21660661482375096], [0.7948348474998488, 0.24213590791713657, 0.21660661482375096], [0.7948348474998488, 0.24213590791713657, 0.21660661482375096], [0.7948348474998488, 0.24213590791713657, 0.21660661482375096], [0.7948348474998488, 0.24213590791713657, 0.21660661482375096], [0.7948348474998488, 0.24213590791713657, 0.21660661482375096]]}

hard_0009

D

hard

{"question_id": "hard_0009", "num_cubes": 7, "difficulty": "hard", "rotation_task": {"axis": "y", "angle": 90, "direction": "clockwise"}, "color_mode": "single", "options": {"A": {"axis": "y", "angle": 150, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "z", "angle": 150, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "z", "angle": 60, "direction": "clockwise", "filename": "choice2.png"}, "D": {"axis": "y", "angle": 90, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "D", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 90\u00b0 clockwise around the Y axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.8551967278436708, 0.7585253145490325, 0.19415100229658983], [0.8551967278436708, 0.7585253145490325, 0.19415100229658983], [0.8551967278436708, 0.7585253145490325, 0.19415100229658983], [0.8551967278436708, 0.7585253145490325, 0.19415100229658983], [0.8551967278436708, 0.7585253145490325, 0.19415100229658983], [0.8551967278436708, 0.7585253145490325, 0.19415100229658983], [0.9401079046287002, 0.7672837735953392, 0.11527091907190404], [0.9401079046287002, 0.7672837735953392, 0.11527091907190404], [0.9401079046287002, 0.7672837735953392, 0.11527091907190404], [0.9401079046287002, 0.7672837735953392, 0.11527091907190404], [0.9401079046287002, 0.7672837735953392, 0.11527091907190404], [0.9401079046287002, 0.7672837735953392, 0.11527091907190404], [0.7444807844476274, 0.6745444483279249, 0.10219379726295288], [0.7444807844476274, 0.6745444483279249, 0.10219379726295288], [0.7444807844476274, 0.6745444483279249, 0.10219379726295288], [0.7444807844476274, 0.6745444483279249, 0.10219379726295288], [0.7444807844476274, 0.6745444483279249, 0.10219379726295288], [0.7444807844476274, 0.6745444483279249, 0.10219379726295288], [0.9035243227757828, 0.6165663228860079, 0.07240056808246018], [0.9035243227757828, 0.6165663228860079, 0.07240056808246018], [0.9035243227757828, 0.6165663228860079, 0.07240056808246018], [0.9035243227757828, 0.6165663228860079, 0.07240056808246018], [0.9035243227757828, 0.6165663228860079, 0.07240056808246018], [0.9035243227757828, 0.6165663228860079, 0.07240056808246018], [1, 0.792987045809197, 0], [1, 0.792987045809197, 0], [1, 0.792987045809197, 0], [1, 0.792987045809197, 0], [1, 0.792987045809197, 0], [1, 0.792987045809197, 0], [0.9885331758143693, 0.9768013434717613, 0], [0.9885331758143693, 0.9768013434717613, 0], [0.9885331758143693, 0.9768013434717613, 0], [0.9885331758143693, 0.9768013434717613, 0], [0.9885331758143693, 0.9768013434717613, 0], [0.9885331758143693, 0.9768013434717613, 0]]}

hard_0010

C

hard

{"question_id": "hard_0010", "num_cubes": 7, "difficulty": "hard", "rotation_task": {"axis": "z", "angle": 120, "direction": "counter-clockwise"}, "color_mode": "single", "options": {"A": {"axis": "y", "angle": 150, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "x", "angle": 30, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "z", "angle": 120, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "x", "angle": 60, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "C", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 120\u00b0 counter-clockwise around the Z axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.5912591786045032, 0.5772573980939392, 0.26530039998381116], [0.5912591786045032, 0.5772573980939392, 0.26530039998381116], [0.5912591786045032, 0.5772573980939392, 0.26530039998381116], [0.5912591786045032, 0.5772573980939392, 0.26530039998381116], [0.5912591786045032, 0.5772573980939392, 0.26530039998381116], [0.5912591786045032, 0.5772573980939392, 0.26530039998381116], [0.6102871856431246, 0.737390488184299, 0.21634342919941066], [0.6102871856431246, 0.737390488184299, 0.21634342919941066], [0.6102871856431246, 0.737390488184299, 0.21634342919941066], [0.6102871856431246, 0.737390488184299, 0.21634342919941066], [0.6102871856431246, 0.737390488184299, 0.21634342919941066], [0.6102871856431246, 0.737390488184299, 0.21634342919941066], [0.6811945875833698, 0.6146322853343551, 0.3877829356538396], [0.6811945875833698, 0.6146322853343551, 0.3877829356538396], [0.6811945875833698, 0.6146322853343551, 0.3877829356538396], [0.6811945875833698, 0.6146322853343551, 0.3877829356538396], [0.6811945875833698, 0.6146322853343551, 0.3877829356538396], [0.6811945875833698, 0.6146322853343551, 0.3877829356538396], [0.49220361084566355, 0.6103786055431945, 0.25501622003654467], [0.49220361084566355, 0.6103786055431945, 0.25501622003654467], [0.49220361084566355, 0.6103786055431945, 0.25501622003654467], [0.49220361084566355, 0.6103786055431945, 0.25501622003654467], [0.49220361084566355, 0.6103786055431945, 0.25501622003654467], [0.49220361084566355, 0.6103786055431945, 0.25501622003654467], [0.5429219317658267, 0.7991183264401669, 0.2638565112826069], [0.5429219317658267, 0.7991183264401669, 0.2638565112826069], [0.5429219317658267, 0.7991183264401669, 0.2638565112826069], [0.5429219317658267, 0.7991183264401669, 0.2638565112826069], [0.5429219317658267, 0.7991183264401669, 0.2638565112826069], [0.5429219317658267, 0.7991183264401669, 0.2638565112826069], [0.5533027070232324, 0.6335317220138555, 0.17594403381109358], [0.5533027070232324, 0.6335317220138555, 0.17594403381109358], [0.5533027070232324, 0.6335317220138555, 0.17594403381109358], [0.5533027070232324, 0.6335317220138555, 0.17594403381109358], [0.5533027070232324, 0.6335317220138555, 0.17594403381109358], [0.5533027070232324, 0.6335317220138555, 0.17594403381109358], [0.6163269032384041, 0.780893682964523, 0.2805245791750635], [0.6163269032384041, 0.780893682964523, 0.2805245791750635], [0.6163269032384041, 0.780893682964523, 0.2805245791750635], [0.6163269032384041, 0.780893682964523, 0.2805245791750635], [0.6163269032384041, 0.780893682964523, 0.2805245791750635], [0.6163269032384041, 0.780893682964523, 0.2805245791750635]]}

hard_0011

C

hard

{"question_id": "hard_0011", "num_cubes": 7, "difficulty": "hard", "rotation_task": {"axis": "z", "angle": 30, "direction": "clockwise"}, "color_mode": "single", "options": {"A": {"axis": "y", "angle": 60, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 60, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "z", "angle": 30, "direction": "clockwise", "filename": "choice2.png"}, "D": {"axis": "z", "angle": 180, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "C", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 30\u00b0 clockwise around the Z axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.14377686554366126, 0.6367317606151666, 0.7567168529903715], [0.14377686554366126, 0.6367317606151666, 0.7567168529903715], [0.14377686554366126, 0.6367317606151666, 0.7567168529903715], [0.14377686554366126, 0.6367317606151666, 0.7567168529903715], [0.14377686554366126, 0.6367317606151666, 0.7567168529903715], [0.14377686554366126, 0.6367317606151666, 0.7567168529903715], [0.21038368127027135, 0.5453050349147281, 0.7372585810919633], [0.21038368127027135, 0.5453050349147281, 0.7372585810919633], [0.21038368127027135, 0.5453050349147281, 0.7372585810919633], [0.21038368127027135, 0.5453050349147281, 0.7372585810919633], [0.21038368127027135, 0.5453050349147281, 0.7372585810919633], [0.21038368127027135, 0.5453050349147281, 0.7372585810919633], [0.3488738853365227, 0.5388147853353188, 0.8753304933958199], [0.3488738853365227, 0.5388147853353188, 0.8753304933958199], [0.3488738853365227, 0.5388147853353188, 0.8753304933958199], [0.3488738853365227, 0.5388147853353188, 0.8753304933958199], [0.3488738853365227, 0.5388147853353188, 0.8753304933958199], [0.3488738853365227, 0.5388147853353188, 0.8753304933958199], [0.2499262781754218, 0.5686905978448709, 0.8668759883284867], [0.2499262781754218, 0.5686905978448709, 0.8668759883284867], [0.2499262781754218, 0.5686905978448709, 0.8668759883284867], [0.2499262781754218, 0.5686905978448709, 0.8668759883284867], [0.2499262781754218, 0.5686905978448709, 0.8668759883284867], [0.2499262781754218, 0.5686905978448709, 0.8668759883284867], [0.17672981047776026, 0.67166447823174, 0.7137292480007824], [0.17672981047776026, 0.67166447823174, 0.7137292480007824], [0.17672981047776026, 0.67166447823174, 0.7137292480007824], [0.17672981047776026, 0.67166447823174, 0.7137292480007824], [0.17672981047776026, 0.67166447823174, 0.7137292480007824], [0.17672981047776026, 0.67166447823174, 0.7137292480007824]]}

hard_0012

A

hard

{"question_id": "hard_0012", "num_cubes": 7, "difficulty": "hard", "rotation_task": {"axis": "y", "angle": 150, "direction": "clockwise"}, "color_mode": "single", "options": {"A": {"axis": "y", "angle": 150, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "x", "angle": 30, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 90, "direction": "clockwise", "filename": "choice2.png"}, "D": {"axis": "y", "angle": 90, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "A", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 150\u00b0 clockwise around the Y axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0, 0.4778919777724893, 0.9454982649327035], [0, 0.4778919777724893, 0.9454982649327035], [0, 0.4778919777724893, 0.9454982649327035], [0, 0.4778919777724893, 0.9454982649327035], [0, 0.4778919777724893, 0.9454982649327035], [0, 0.4778919777724893, 0.9454982649327035], [0, 0.5960933737140911, 0.9375010615942732], [0, 0.5960933737140911, 0.9375010615942732], [0, 0.5960933737140911, 0.9375010615942732], [0, 0.5960933737140911, 0.9375010615942732], [0, 0.5960933737140911, 0.9375010615942732], [0, 0.5960933737140911, 0.9375010615942732], [0.1505513311767221, 0.6613436196384403, 0.8771224067494254], [0.1505513311767221, 0.6613436196384403, 0.8771224067494254], [0.1505513311767221, 0.6613436196384403, 0.8771224067494254], [0.1505513311767221, 0.6613436196384403, 0.8771224067494254], [0.1505513311767221, 0.6613436196384403, 0.8771224067494254], [0.1505513311767221, 0.6613436196384403, 0.8771224067494254], [0, 0.8129120547021856, 0.8188623207553641], [0, 0.8129120547021856, 0.8188623207553641], [0, 0.8129120547021856, 0.8188623207553641], [0, 0.8129120547021856, 0.8188623207553641], [0, 0.8129120547021856, 0.8188623207553641], [0, 0.8129120547021856, 0.8188623207553641], [0.03377535132646786, 0.8187625099841296, 0.7357356428880986], [0.03377535132646786, 0.8187625099841296, 0.7357356428880986], [0.03377535132646786, 0.8187625099841296, 0.7357356428880986], [0.03377535132646786, 0.8187625099841296, 0.7357356428880986], [0.03377535132646786, 0.8187625099841296, 0.7357356428880986], [0.03377535132646786, 0.8187625099841296, 0.7357356428880986]]}

hard_0013

B

hard

{"question_id": "hard_0013", "num_cubes": 8, "difficulty": "hard", "rotation_task": {"axis": "y", "angle": 180, "direction": "counter-clockwise"}, "color_mode": "single", "options": {"A": {"axis": "z", "angle": 30, "direction": "counter-clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 180, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "y", "angle": 150, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "z", "angle": 90, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "B", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 180\u00b0 counter-clockwise around the Y axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.4931756758755902, 0, 0.8111301054611286], [0.4931756758755902, 0, 0.8111301054611286], [0.4931756758755902, 0, 0.8111301054611286], [0.4931756758755902, 0, 0.8111301054611286], [0.4931756758755902, 0, 0.8111301054611286], [0.4931756758755902, 0, 0.8111301054611286], [0.6788906152229826, 0.010734475271865801, 0.9905009429815813], [0.6788906152229826, 0.010734475271865801, 0.9905009429815813], [0.6788906152229826, 0.010734475271865801, 0.9905009429815813], [0.6788906152229826, 0.010734475271865801, 0.9905009429815813], [0.6788906152229826, 0.010734475271865801, 0.9905009429815813], [0.6788906152229826, 0.010734475271865801, 0.9905009429815813], [0.7138631990904896, 0.20749749888862204, 1], [0.7138631990904896, 0.20749749888862204, 1], [0.7138631990904896, 0.20749749888862204, 1], [0.7138631990904896, 0.20749749888862204, 1], [0.7138631990904896, 0.20749749888862204, 1], [0.7138631990904896, 0.20749749888862204, 1], [0.8820723251046112, 0.29459493336601184, 0.8657696492783163], [0.8820723251046112, 0.29459493336601184, 0.8657696492783163], [0.8820723251046112, 0.29459493336601184, 0.8657696492783163], [0.8820723251046112, 0.29459493336601184, 0.8657696492783163], [0.8820723251046112, 0.29459493336601184, 0.8657696492783163], [0.8820723251046112, 0.29459493336601184, 0.8657696492783163], [1, 0.17813920063542982, 0.9776833900426909], [1, 0.17813920063542982, 0.9776833900426909], [1, 0.17813920063542982, 0.9776833900426909], [1, 0.17813920063542982, 0.9776833900426909], [1, 0.17813920063542982, 0.9776833900426909], [1, 0.17813920063542982, 0.9776833900426909]]}

hard_0014

D

hard

{"question_id": "hard_0014", "num_cubes": 6, "difficulty": "hard", "rotation_task": {"axis": "z", "angle": 120, "direction": "clockwise"}, "color_mode": "single", "options": {"A": {"axis": "x", "angle": 30, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 120, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 180, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "z", "angle": 120, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "D", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 120\u00b0 clockwise around the Z axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.5581121597225462, 0.2698802654867306, 0.23004340598941894], [0.5581121597225462, 0.2698802654867306, 0.23004340598941894], [0.5581121597225462, 0.2698802654867306, 0.23004340598941894], [0.5581121597225462, 0.2698802654867306, 0.23004340598941894], [0.5581121597225462, 0.2698802654867306, 0.23004340598941894], [0.5581121597225462, 0.2698802654867306, 0.23004340598941894], [0.4337097870687866, 0.10837121436602515, 0.308178224391082], [0.4337097870687866, 0.10837121436602515, 0.308178224391082], [0.4337097870687866, 0.10837121436602515, 0.308178224391082], [0.4337097870687866, 0.10837121436602515, 0.308178224391082], [0.4337097870687866, 0.10837121436602515, 0.308178224391082], [0.4337097870687866, 0.10837121436602515, 0.308178224391082], [0.5930079471486808, 0.1668899334385089, 0.2602130708315644], [0.5930079471486808, 0.1668899334385089, 0.2602130708315644], [0.5930079471486808, 0.1668899334385089, 0.2602130708315644], [0.5930079471486808, 0.1668899334385089, 0.2602130708315644], [0.5930079471486808, 0.1668899334385089, 0.2602130708315644], [0.5930079471486808, 0.1668899334385089, 0.2602130708315644], [0.7172838562913332, 0.27417924410464495, 0.43537536697945994], [0.7172838562913332, 0.27417924410464495, 0.43537536697945994], [0.7172838562913332, 0.27417924410464495, 0.43537536697945994], [0.7172838562913332, 0.27417924410464495, 0.43537536697945994], [0.7172838562913332, 0.27417924410464495, 0.43537536697945994], [0.7172838562913332, 0.27417924410464495, 0.43537536697945994], [0.5872898829027764, 0.13779527648838458, 0.3278152247594557], [0.5872898829027764, 0.13779527648838458, 0.3278152247594557], [0.5872898829027764, 0.13779527648838458, 0.3278152247594557], [0.5872898829027764, 0.13779527648838458, 0.3278152247594557], [0.5872898829027764, 0.13779527648838458, 0.3278152247594557], [0.5872898829027764, 0.13779527648838458, 0.3278152247594557], [0.7340228407860092, 0.14868636837888452, 0.171307621109969], [0.7340228407860092, 0.14868636837888452, 0.171307621109969], [0.7340228407860092, 0.14868636837888452, 0.171307621109969], [0.7340228407860092, 0.14868636837888452, 0.171307621109969], [0.7340228407860092, 0.14868636837888452, 0.171307621109969], [0.7340228407860092, 0.14868636837888452, 0.171307621109969]]}

hard_0015

D

hard

{"question_id": "hard_0015", "num_cubes": 7, "difficulty": "hard", "rotation_task": {"axis": "x", "angle": 60, "direction": "counter-clockwise"}, "color_mode": "single", "options": {"A": {"axis": "y", "angle": 180, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "z", "angle": 180, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "z", "angle": 120, "direction": "clockwise", "filename": "choice2.png"}, "D": {"axis": "x", "angle": 60, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "D", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 60\u00b0 counter-clockwise around the X axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.6670753958434186, 0.8271766316728075, 0.1337448011225024], [0.6670753958434186, 0.8271766316728075, 0.1337448011225024], [0.6670753958434186, 0.8271766316728075, 0.1337448011225024], [0.6670753958434186, 0.8271766316728075, 0.1337448011225024], [0.6670753958434186, 0.8271766316728075, 0.1337448011225024], [0.6670753958434186, 0.8271766316728075, 0.1337448011225024], [0.7263211487712814, 0.7045258175006923, 0], [0.7263211487712814, 0.7045258175006923, 0], [0.7263211487712814, 0.7045258175006923, 0], [0.7263211487712814, 0.7045258175006923, 0], [0.7263211487712814, 0.7045258175006923, 0], [0.7263211487712814, 0.7045258175006923, 0], [0.8659907295716578, 0.540239633140165, 0], [0.8659907295716578, 0.540239633140165, 0], [0.8659907295716578, 0.540239633140165, 0], [0.8659907295716578, 0.540239633140165, 0], [0.8659907295716578, 0.540239633140165, 0], [0.8659907295716578, 0.540239633140165, 0], [0.9592355465924668, 0.3532088356469776, 0.18032973681413644], [0.9592355465924668, 0.3532088356469776, 0.18032973681413644], [0.9592355465924668, 0.3532088356469776, 0.18032973681413644], [0.9592355465924668, 0.3532088356469776, 0.18032973681413644], [0.9592355465924668, 0.3532088356469776, 0.18032973681413644], [0.9592355465924668, 0.3532088356469776, 0.18032973681413644], [1, 0.2779650346473658, 0.2027958061968561], [1, 0.2779650346473658, 0.2027958061968561], [1, 0.2779650346473658, 0.2027958061968561], [1, 0.2779650346473658, 0.2027958061968561], [1, 0.2779650346473658, 0.2027958061968561], [1, 0.2779650346473658, 0.2027958061968561]]}

hard_0016

C

hard

{"question_id": "hard_0016", "num_cubes": 6, "difficulty": "hard", "rotation_task": {"axis": "x", "angle": 90, "direction": "counter-clockwise"}, "color_mode": "single", "options": {"A": {"axis": "z", "angle": 180, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 150, "direction": "counter-clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 90, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "z", "angle": 30, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "C", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 90\u00b0 counter-clockwise around the X axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[1, 0.9513474321219664, 0.6628073254089775], [1, 0.9513474321219664, 0.6628073254089775], [1, 0.9513474321219664, 0.6628073254089775], [1, 0.9513474321219664, 0.6628073254089775], [1, 0.9513474321219664, 0.6628073254089775], [1, 0.9513474321219664, 0.6628073254089775], [0.8109587098086414, 0.8658200634950707, 0.6304189968011501], [0.8109587098086414, 0.8658200634950707, 0.6304189968011501], [0.8109587098086414, 0.8658200634950707, 0.6304189968011501], [0.8109587098086414, 0.8658200634950707, 0.6304189968011501], [0.8109587098086414, 0.8658200634950707, 0.6304189968011501], [0.8109587098086414, 0.8658200634950707, 0.6304189968011501], [0.721748462715017, 0.8828264155669265, 0.5441263713746258], [0.721748462715017, 0.8828264155669265, 0.5441263713746258], [0.721748462715017, 0.8828264155669265, 0.5441263713746258], [0.721748462715017, 0.8828264155669265, 0.5441263713746258], [0.721748462715017, 0.8828264155669265, 0.5441263713746258], [0.721748462715017, 0.8828264155669265, 0.5441263713746258], [0.7601852334704474, 0.7348543105300904, 0.6337360279620681], [0.7601852334704474, 0.7348543105300904, 0.6337360279620681], [0.7601852334704474, 0.7348543105300904, 0.6337360279620681], [0.7601852334704474, 0.7348543105300904, 0.6337360279620681], [0.7601852334704474, 0.7348543105300904, 0.6337360279620681], [0.7601852334704474, 0.7348543105300904, 0.6337360279620681], [0.766351030164667, 0.6382890091400055, 0.6810548247172097], [0.766351030164667, 0.6382890091400055, 0.6810548247172097], [0.766351030164667, 0.6382890091400055, 0.6810548247172097], [0.766351030164667, 0.6382890091400055, 0.6810548247172097], [0.766351030164667, 0.6382890091400055, 0.6810548247172097], [0.766351030164667, 0.6382890091400055, 0.6810548247172097], [0.6704338788601, 0.5328160016154382, 0.6705451317121982], [0.6704338788601, 0.5328160016154382, 0.6705451317121982], [0.6704338788601, 0.5328160016154382, 0.6705451317121982], [0.6704338788601, 0.5328160016154382, 0.6705451317121982], [0.6704338788601, 0.5328160016154382, 0.6705451317121982], [0.6704338788601, 0.5328160016154382, 0.6705451317121982]]}

hard_0017

C

hard

{"question_id": "hard_0017", "num_cubes": 5, "difficulty": "hard", "rotation_task": {"axis": "x", "angle": 120, "direction": "clockwise"}, "color_mode": "single", "options": {"A": {"axis": "z", "angle": 30, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "z", "angle": 60, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 120, "direction": "clockwise", "filename": "choice2.png"}, "D": {"axis": "y", "angle": 90, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "C", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 120\u00b0 clockwise around the X axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.5096488036930084, 0.20085311126488928, 0.9186918084516003], [0.5096488036930084, 0.20085311126488928, 0.9186918084516003], [0.5096488036930084, 0.20085311126488928, 0.9186918084516003], [0.5096488036930084, 0.20085311126488928, 0.9186918084516003], [0.5096488036930084, 0.20085311126488928, 0.9186918084516003], [0.5096488036930084, 0.20085311126488928, 0.9186918084516003], [0.3324536858891124, 0.1406690613132904, 0.8568398186128255], [0.3324536858891124, 0.1406690613132904, 0.8568398186128255], [0.3324536858891124, 0.1406690613132904, 0.8568398186128255], [0.3324536858891124, 0.1406690613132904, 0.8568398186128255], [0.3324536858891124, 0.1406690613132904, 0.8568398186128255], [0.3324536858891124, 0.1406690613132904, 0.8568398186128255], [0.2932651405066079, 0.011868480445363622, 0.9765787965584057], [0.2932651405066079, 0.011868480445363622, 0.9765787965584057], [0.2932651405066079, 0.011868480445363622, 0.9765787965584057], [0.2932651405066079, 0.011868480445363622, 0.9765787965584057], [0.2932651405066079, 0.011868480445363622, 0.9765787965584057], [0.2932651405066079, 0.011868480445363622, 0.9765787965584057], [0.3631332080238329, 0.18904793424205876, 1], [0.3631332080238329, 0.18904793424205876, 1], [0.3631332080238329, 0.18904793424205876, 1], [0.3631332080238329, 0.18904793424205876, 1], [0.3631332080238329, 0.18904793424205876, 1], [0.3631332080238329, 0.18904793424205876, 1]]}

hard_0018

C

hard

{"question_id": "hard_0018", "num_cubes": 6, "difficulty": "hard", "rotation_task": {"axis": "x", "angle": 90, "direction": "counter-clockwise"}, "color_mode": "single", "options": {"A": {"axis": "z", "angle": 150, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "y", "angle": 120, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "x", "angle": 90, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "y", "angle": 180, "direction": "clockwise", "filename": "choice3.png"}}, "answer": "C", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 90\u00b0 counter-clockwise around the X axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.9106044471099551, 0.7909344028805829, 0.26845635830495396], [0.9106044471099551, 0.7909344028805829, 0.26845635830495396], [0.9106044471099551, 0.7909344028805829, 0.26845635830495396], [0.9106044471099551, 0.7909344028805829, 0.26845635830495396], [0.9106044471099551, 0.7909344028805829, 0.26845635830495396], [0.9106044471099551, 0.7909344028805829, 0.26845635830495396], [0.8464899881423561, 0.7525637706742294, 0.18759757926022758], [0.8464899881423561, 0.7525637706742294, 0.18759757926022758], [0.8464899881423561, 0.7525637706742294, 0.18759757926022758], [0.8464899881423561, 0.7525637706742294, 0.18759757926022758], [0.8464899881423561, 0.7525637706742294, 0.18759757926022758], [0.8464899881423561, 0.7525637706742294, 0.18759757926022758], [0.7112496977432072, 0.5679507223743246, 0.02021454831671557], [0.7112496977432072, 0.5679507223743246, 0.02021454831671557], [0.7112496977432072, 0.5679507223743246, 0.02021454831671557], [0.7112496977432072, 0.5679507223743246, 0.02021454831671557], [0.7112496977432072, 0.5679507223743246, 0.02021454831671557], [0.7112496977432072, 0.5679507223743246, 0.02021454831671557]]}

hard_0019

C

hard

{"question_id": "hard_0019", "num_cubes": 7, "difficulty": "hard", "rotation_task": {"axis": "z", "angle": 180, "direction": "counter-clockwise"}, "color_mode": "single", "options": {"A": {"axis": "x", "angle": 180, "direction": "clockwise", "filename": "choice0.png"}, "B": {"axis": "x", "angle": 90, "direction": "clockwise", "filename": "choice1.png"}, "C": {"axis": "z", "angle": 180, "direction": "counter-clockwise", "filename": "choice2.png"}, "D": {"axis": "z", "angle": 30, "direction": "counter-clockwise", "filename": "choice3.png"}}, "answer": "C", "question": "<Image 1> is a shape made of connected, colored cubes, rendered from the front. Imagine rotating this shape 180\u00b0 counter-clockwise around the Z axis. Which of the following options in <Image 2> represents the shape after the rotation?", "colors": [[0.556361688137599, 0.4077171340161099, 0.09154372362846963], [0.556361688137599, 0.4077171340161099, 0.09154372362846963], [0.556361688137599, 0.4077171340161099, 0.09154372362846963], [0.556361688137599, 0.4077171340161099, 0.09154372362846963], [0.556361688137599, 0.4077171340161099, 0.09154372362846963], [0.556361688137599, 0.4077171340161099, 0.09154372362846963], [0.5042829583472703, 0.5051223002755114, 0.23270482391032243], [0.5042829583472703, 0.5051223002755114, 0.23270482391032243], [0.5042829583472703, 0.5051223002755114, 0.23270482391032243], [0.5042829583472703, 0.5051223002755114, 0.23270482391032243], [0.5042829583472703, 0.5051223002755114, 0.23270482391032243], [0.5042829583472703, 0.5051223002755114, 0.23270482391032243], [0.34314653594180056, 0.6265641293753502, 0.21852555178594274], [0.34314653594180056, 0.6265641293753502, 0.21852555178594274], [0.34314653594180056, 0.6265641293753502, 0.21852555178594274], [0.34314653594180056, 0.6265641293753502, 0.21852555178594274], [0.34314653594180056, 0.6265641293753502, 0.21852555178594274], [0.34314653594180056, 0.6265641293753502, 0.21852555178594274], [0.5040285217296078, 0.5671509164416048, 0.1282540108000623], [0.5040285217296078, 0.5671509164416048, 0.1282540108000623], [0.5040285217296078, 0.5671509164416048, 0.1282540108000623], [0.5040285217296078, 0.5671509164416048, 0.1282540108000623], [0.5040285217296078, 0.5671509164416048, 0.1282540108000623], [0.5040285217296078, 0.5671509164416048, 0.1282540108000623], [0.3707342922386145, 0.6577323596106242, 0.23770930217519978], [0.3707342922386145, 0.6577323596106242, 0.23770930217519978], [0.3707342922386145, 0.6577323596106242, 0.23770930217519978], [0.3707342922386145, 0.6577323596106242, 0.23770930217519978], [0.3707342922386145, 0.6577323596106242, 0.23770930217519978], [0.3707342922386145, 0.6577323596106242, 0.23770930217519978]]}