Wednesday, April 7, 2010

Cut the Cake


Happy Birthday, Kyle! 
With 3 straight cuts through a cylindrical cake, make 8 equal-sized slices. 

There are two solutions.

(Hint: you are allowed to move some or all of the cake)






Solution:
Both solutions involve making two normal vertical cuts to make quarters.  For the third cut, one way is to hold the knife parallel to the ground and cut the cake into top and bottom halves.  However this results in some people not getting any frosting.  The alternative is to rearrange the quarters - either stack them on top of each other, or line them up in one long line - so that you can cut through all of them with one more long vertical cut. 

7 comments:

  1. 1) quartered like you would a pie, and then halved widthwise (through the equator)

    2) I will think about the second way on my walk

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  2. For the sake of all the cake eaters, try to make all the pieces the same shape as well as the same size.

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  3. Well, since we are allowed to move some or all of the cake, that opens up tons of possibilities.
    I'm thinking to cut the cake in half, stack them on top of one another, then cut it in half again (and then repeat the process). This way, three cuts result in eight congruent pieces.

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  4. Nice solution, that's what I was thinking

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  5. Mine are the same shape & size! They are perhaps not equitably frosted, but then, stacking the quartered pieces will mess up the frosting anyhow. Better to cut first and add frosting later.

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  6. I love your consideration of tastiness in your answer, Strong :)

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  7. Oh...it never even occurred to me that I should be equitable with the frosting

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