Home > Shapes
| The Bun Problem (Posted on 2004-05-07) |
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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.)
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Submitted by Gamer
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Rating: 2.0000 (5 votes)
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Solution:
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First, cut the 5 bun in half. Then put the 3 bun so its center is on the 4 bun's center. Then cut the diameter of the 4 bun, but stop and cut "around" the 3 bun when you get to it. This should form a C shaped piece and a piece shaped like 2 fused half circles. Two children each get a half-5 bun piece, One child gets the 3 bun and the C shaped piece from the 4 bun, and one child gets the remaining piece.
Since both halves are the same, and when the 3 bun is placed in the C shaped piece, it looks exactly like the piece that looks like half a 3 bun and half a 4 bun fused together, all that needs to be proven is the two sets of pieces are congruent. This is easily done the 4-bun half (16/2 pi square inches) added on to the 3-bun half (9/2 pi square inches) gives the 5-bun half (15/2 pi square inches) which shows that the two sets are equal. |
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