[Illustration]
Miss Charity Lockyer clearly must have had a trick up her sleeve, and I
think it highly probable that it was conceived on the following lines.
She proposed that ten lumps of sugar should be placed in three teacups,
so that there should be an odd number of lumps in every cup. The
illustration perhaps shows Miss Charity's answer, and the figures on the
cups indicate the number of lumps that have been separately placed in
them. By placing the cup that holds one lump inside the one that holds
two lumps, it can be correctly stated that every cup contains an odd
number of lumps. One cup holds seven lumps, another holds one lump, while
the third cup holds three lumps. It is evident that if a cup contains
another cup it also contains the contents of that second cup.
There are in all fifteen different solutions to this puzzle. Here they
are:--
1 0 9 1 4 5 9 0 1
3 0 7 7 0 3 7 2 1
1 2 7 5 2 3 5 4 1
5 0 5 3 4 3 3 6 1
3 2 5 1 6 3 1 8 1
The first two numbers in a triplet represent respectively the number of
lumps to be placed in the inner and outer of the two cups that are placed
one inside the other. It will be noted that the outer cup of the pair may
itself be empty.