55 The Three Teacups
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.