The Three Teacups
(
THE SQUIRE'S CHRISTMAS PUZZLE PARTY)
One young lady—of whom our fair historian records with delightful inconsequence: "This Miss Charity Lockyer has since been married to a curate from Taunton Vale"—placed three empty teacups on a table, and challenged anybody to put ten lumps of sugar in them so that there would be an odd number of lumps in every cup. "One young man, who has been to Oxford University, and is studying the law, declared with some heat that, beyond a doubt, there was no possible way of doing it, and he offered to give proof of the fact to the company." It must have been interesting to see his face when he was shown Miss Charity's correct answer.
Answer:
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.
Informational
