THE CANTERBURY PUZZLES
kissed a male ; no man kissed a married woman except his own
wife ; all the bachelors and boys kissed all the maidens and girls
twice ; the widower did not kiss anybody, and the widows did not
kiss eaeh other. Every kiss was returned, and the double perform-
ance was to count as one kiss. In making a list of the company, we
can leave out the widower altogether, because he took no part in
the osculatory exercise.
7 Married couples
14
3 Widows
3
12 Bachelors and Boys .... 12
10 Maidens and Girls
10
Total
39 Persons
Now, if everyone of these 39 persons kissed everybody else
once, the number of kisses would be 741, and if the 12 bachelors
and boys each kissed the 10 maidens and girls once again, we must
add 120, making a total of 861 kisses. But as no married man
kissed a married woman other than his own wife, we must deduct
42 kisses ; as no male kissed another male, we must deduct 171
kisses ; and as no widow kissed another widow, we must deduct 3
kisses. We have, therefore, to deduct 42+ 171 +3 = 216 kisses
from the above total of 861, and the result, 645, represents exactly
the number of kisses that were actually given under the mistletoe
bough.
61.—
The Silver Cubes.
There is no limit to the number of different dimensions that will
give two cubes whose sum shall be exactly seventeen cubic inches.
Here is the answer in the smallest possible numbers. One of the
silver cubes must measure 2f^Mf inches along each edge, and the
other must measure IMS? inch. If the reader likes to undertake
the task of cubing each number (that is, multiply each number twice
by itself) he will find that when added together the contents exactly
equal seventeen cubic inches. See also No. 20, " The Puzzle of
the Doctor of Physic."
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