Lockyer clearly must have had a trick
sleeve, and I
think it highly probable that it was conceived on the following
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.
illustration perhaps shows Miss Charity's answer, and the figures on
cups indicate the number of lumps that have been separately placed in
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,
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
|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
lumps to be placed in the inner and outer of the two cups that are
one inside the other.
It will be noted
that the outer cup of the pair
itself be empty.