nce under the
mistletoe, with the following additions and exceptions: No male 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 each other. Every kiss
was returned, and the double performance 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 every one 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 2-23278/40831 inches along each edge, and the other must measure
11663/40831 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."

THE ADVENTURES OF THE PUZZLE CLUB

62.--_The Ambiguous Photograph._

One by one the members of the Club succeeded in discovering the key to
the mystery of the Ambiguous Photograph, except Churton, who was at
length persuaded to "give it up." Herbert Baynes then pointed out to him
that the coat that Lord Marksford was carrying over his arm was a lady's
coat, because the buttons are on the left side, whereas a man's coat
always has the buttons on the right-hand side. Lord Marksford would not
be likely to walk about the streets of Paris with a lady's coat ove