27 small cubes of size 1x1x1 are assembled into one large cube of size 3x3x3. How many small cubes does the plane orthogonal to the diagonal of the large cube cut ?

Question

anonymous · Answer

The plane orthogonal to the diagonal will cut the off diagonal cubes, this should be 3.

anonymous · Answer

How? The plane orthogonal to the diagonal of the larger cube doesn’t form a square…so one can’t assume that it just cuts off the diagonal cubes. Plus, what about the cubes inside the solid?
	Please advise. Thanks! :)

anonymous · Answer

Interesting, ... so  by diagonal you mean the longest diagonal?

anonymous · Answer

Yes. It's difficult to visualize what 2D shape is formed by the intersection of the cube and the orthogonal plane to the diagonal...I think it forms a kite shape with vertices at two corners and two midpoints of two of the edges on the cube, but I'm not sure.

anonymous · Answer

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anonymous · Answer

Yes :)

anonymous · Answer

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This is not the orthogonal?