Cube Pile-Invisible Cubes

Here is a pile of identical cubes stacked in the corner of a room. How many of the cubes in the pile are not visible?




Show/Hide Solution

One way to count the hidden cubes is to count the number of cubes each of the visible cubes is sitting on. The top cube is sitting on 4 cubes. The two cubes in the second layer are each sitting on 3 cubes, and so on. Add them up: 4 + (3+3) + (2+2+2) + (1+1+1+1) = 20.

So there are 20 hidden cubes.

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