Question 608260: Mr.Algebra baked a cake for the Midwest Mathematics Convention. He designed the cake in the shape of a big cube. As he was carrying the cake over to frost it, he dropped it in the vat of frosting. Amazingly, athe cake stayed in one piece, but all 6 sides were frosted. One mathematic suggested the cake be cut into cube shaped pieces, all the same size. That way, some people could have a piece with no frosting, 1 side frosted, 2 sides frosted, or 3 sides frosted. Another mathematician suggested, "Cut the cake so that the number of pieces with no frosting is eight times more than the number of pieces with 3 sides frosted. Then you will have the exact number of pieces of cake as there are mathemeticians in this room." Find out how many mathematicians were at the convention.
Answer by solver91311(24713)   (Show Source):
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There are 8 corners on the cube, hence 8 pieces of cake with 3 sides frosted. That means 64 pieces with no frosting, forming an inner cube that is 4 X 4 X 4. Hence the outer cube, the one with all the frosting, is 6 X 6 X 6.
John
My calculator said it, I believe it, that settles it
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