Take a circular slice of potato, place it on the table, and see into how
large a number of pieces you can divide it with six cuts of a knife. Of
course you must not readjust the pieces or pile them after a cut. What
is the greatest number of pieces you can make?
[Illustration:
--------
/ \ 1/ \
/ \ 2 \/ 3 / \
/ \ /\ / \
/ \ 4 \/ 5\/ 6 / \
| \ /\ /\ / |
\ 7\/ 8\/ 9\/10 /
\ /\ /\ /\ /
\/11\/12\/13\/
\ /\ /\ /
\/14\/15\/
\ /\ /
\/16\/
-----
]
The illustration shows how to make sixteen pieces. This can, of course,
be easily beaten.