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 The Bun Problem (Posted on 2004-05-07)
Here is a good shape problem I heard about recently:

There are 3 buns with sprinkles on the top that 4 people want to share. The buns have a radius of 3 inches, 4 inches and 5 inches, and although the people know where the center of each bun is, they don't know anything else about the buns, and all they have is a knife to divide the buns.

What is the fewest number of pieces required to let each person have the same area of bun? (Note that each cut must be from top to bottom; horizontal cuts would result in uneven sprinkle distribution. The cuts don't need to be straight.)

 See The Solution Submitted by Gamer Rating: 2.0000 (5 votes)

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 re: r^2 or r^3? | Comment 13 of 26 |
(In reply to r^2 or r^3? by ronen)

If the buns are spheres instead of cylindars, then the minimum number of pieces would be 6.     The volumes would be in the ratio of   27:64:125  which totals 216.  One fourth of 216 is 54.  So making appropriately measured radial cuts would be:

Bun     Sizes
27       27
64       54    10
128      54    54    17

Six easy pieces.   But what I can't figure out is if the sprinkles will come off when the spherical buns are dunked in a cup of coffee.

 Posted by Larry on 2004-05-08 08:36:56

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