The arrangement of colored cubes

Geometry Level 3

The following 3D image consists of four cubes of yellow, red, green and blue colors.

The image below shows 12 possible 2D views of the 3D image above with the diagrams A to L. How many of the 2D views are correct?


The answer is 6.

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1 solution

Marta Reece
Mar 14, 2018

The correct views are C, D, F, H, I, and J.

If the square in the corner of the 2D view, the one in contact with two other squares, is yellow, green, or blue, there is only one orientation from which the solid appears to be three squares. Each of these is presented as a possible options. They are C for yellow, I for blue, and J for green.

But if the red color is in the corner, there are three possible views, all of which are again provided as options. They are D for looking from the left, F for looking from the back, and H for looking from below.

The problem could have been made more interesting still if other options were also provided, say with red in the corner but the wrong organization of the other colors. But it is a very nice problem. Thank you.

Marta Reece - 3 years, 2 months ago

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