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# Triangle ABC watch

1. A cake in the form of a cube falls into a vat of frosting and comes out frosted on all six faces. The cake is then cut into smaller cubes, each one inch on an edge. The cake is cut so that the number of pieces having frosting on three faces will be one-eighth the number of pieces having no frosting at all. There are to be exactly enough pieces of cake for everyone. How many people will receive a piece of cake with frosting on exactly three faces? On exactly two faces? On exactly one face? On no faces? How large was the original cake?
2. Remember that only corner pieces will have frosting on three of their faces; pieces from edges (but not on corners) on two of theirs, and pieces from the middles of a face on only one.
How many "corner pieces" are there on the original cake? So how many pieces have no frosting? Can you then do the rest?
3. (Original post by drmath)
A cake in the form of a cube falls into a vat of frosting and comes out frosted on all six faces. The cake is then cut into smaller cubes, each one inch on an edge. The cake is cut so that the number of pieces having frosting on three faces will be one-eighth the number of pieces having no frosting at all. There are to be exactly enough pieces of cake for everyone. How many people will receive a piece of cake with frosting on exactly three faces? On exactly two faces? On exactly one face? On no faces? How large was the original cake?
This used to be an Intermediate coursework task for GCSE, where students were expected to find general formulae for the number of cubes with 0, 1, 2 and 3 frostings. In this case we have a cube of side 6 with 8, 48, 96 and 64 smaller cubes with 3, 2, 1 and zero frostings respectively.
4. Triangle ABC?!
5. (Original post by generalebriety)
Triangle ABC?!
>_>

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