# Solution

(related to Problem: The Bun Puzzle)

The secret of the bun puzzle lies in the fact that, with the relative dimensions of the circles as given, the three diameters will form a right-angled triangle, as shown by $A, B, C.$ It follows that the two smaller buns are exactly equal to the large bun. Therefore, if we give David and Edgar the two halves marked $D$ and $E,$ they will have their fair shares — one quarter of the confectionery each. Then if we place the small bun, $H,$ on the top of the remaining one and trace its circumference in the manner shown, Fred's piece, $F,$ will exactly equal Harry's small bun, $H,$ with the addition of the piece marked $G$ — half the rim of the other. Thus each boy gets an exactly equal share, and there are only five pieces necessary.

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### References

#### Project Gutenberg

1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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