Can you solve this simple geometric puzzle?
You have 8 cubes of 4 different colors, 2 cubes of each color. Can you think of a way of combining the 8 cubes to make a single cube such that each face of the larger cube has all 4 colors?
After I thought of this problem, I was on the verge of making a model to solve it, but then realized that if you think about it the right way, you can solve it in your head.
Here is a hint. Instead of working on the colors for a given face, think of how a given color can be distributed to all 6 faces.
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5 Answers
Put 4 cubes on the bottom and then criss-cross the colors on top then you will have 6 sides showing all 4 colors.
Each set of same color cubes only touch at a corner.
I’ trying to visualize it. But I think this will work.
Start with all the cubes in the same orientation and stack them to form the larger cube. It will look like the smaller cube.
While keeping the bottom fixed, rotate the top half 180 degrees.
Next,
While keeping one side fixed, rotate the other side 180 degrees.
I cannot prove it but in my head it sure looks like it works. .
I am not following what you are saying. Maybe I did not state this clearly enough. The cubes are each of a single color, two each for each of the four colors.
@filmfann and @Pandora got it right. The two cubes of a given color are placed diagonally opposite each other in the larger cube.
This problem has only one solution.
From @Pandora ‘s answer, you can see that arranging the colors for one face determines where the other cubes are placed, thus determining the way that the 4 colors of the other faces are arranged.
It turns out that the 6 faces of the larger cube each have a different ordering of the 4 colors. Since there are only 6 ways to arrange the 4 colors, that is all there is.
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