[Illustration
. .
. .
_ . .
. |\ A .
| \
. C | \ |
| \
. | \ /
. |______________________\/
| |
. .
. B .
. .
. .
-
_
. | .
. | .
. | .
|
|
| D | E |
|
|
. | .
. | .
. | .
_
_
. | .
. -+- .
. . . .
- -
.
| G| F | |
- -
. . . .
. - _ _ - .
. | .
-
-+-
. .
- -
.
| H |
- -
. .
- _ _ -
]
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.