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CompuChip

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Maybe I am missing something here, but how can you cut an 8 x 8 cake into squares with total area 65?How the cake should be cut into equal 65 squares [...] Each piece should be 1 square foot size.

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CompuChip

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OK, if you start making extra assumptions you can.[... answer ...]

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GT

3rd dimension is not included in the puzzle. Just consider it a flat piece (May be a bread).

CompuChip

Banach-Tarski requieres a lot of cuts, I suppose.

Please note: A square can have no more than 2 pieces, i.e. no more than one cut.

Though it deals with a paradox.

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This still doesn't answer the most basic question raised:I am afraid I was not able to form the quize well.

...

Though it deals with a paradox.

In your question, you stipulate that each piece should be 1 square foot in size. And you say that there should be 65 pieces. This means there MUST be a total of 65 square feet. However, you state that the cake is 8 feet x 8 feet, meaning that there are only 64 square feet of cake available!

Therefore the answer is that they should go out and purchase 1 extra square foot of cake.

But beyond that, you state something that I simply don't understand-- you say "A square can have no more than 2 pieces". What does that mean? You say "no more than one cut", but that also makes no sense. By definition, in order to create a square, you must spend at a minimum

You mention that there is a paradox involved, so perhaps we're meant to divide the cake using some mathematical paradox, like dividing by 0 or something. But the facts stand-- you

DaveE

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I think the OP has in mind the puzzle in which a shape of area 64 is cut and reassembled to make a shape which seems to have an area of 65. Here is an example:

http://brainden.com/forum/index.php?showtopic=139".

If that is the case, then there are some issues with the OP's statement of the problem. While it is true that you might fool some of the people some of the time by showing them that upper quadrilateral and calling it a triangle. However, you cannot fool all of the people all of the time by handing out 65 pieces of 1 foot square cake.

http://brainden.com/forum/index.php?showtopic=139".

If that is the case, then there are some issues with the OP's statement of the problem. While it is true that you might fool some of the people some of the time by showing them that upper quadrilateral and calling it a triangle. However, you cannot fool all of the people all of the time by handing out 65 pieces of 1 foot square cake.

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CompuChip

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