THE BUN PUZZLE.
(
Various Dissection Puzzles)
THE three circles represent three buns, and it is simply required to
show how these may be equally divided among four boys. The buns must be
regarded as of equal thickness throughout and of equal thickness to each
other. Of course, they must be cut into as few pieces as possible. To
simplify it I will state the rather surprising fact that only five
pieces are necessary, from which it will be seen that one boy gets his
share in two pieces and the other three receive theirs in a single
piece. I am aware that this statement "gives away" the puzzle, but it
should not destroy its interest to those who like to discover the
"reason why."
Answer:
[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.
