Everybody was found
to have kissed everybody else
mistletoe, with the following additions and exceptions:
No male kissed
male; no man kissed a married woman except his own wife;
bachelors and boys kissed all the maidens and girls twice;
did not kiss anybody, and the widows did not kiss each other.
was returned, and the double performance was to count as one
making a list of the
company, we can leave out the widower altogether,
because he took no part in the osculatory exercise.
Now, if every one
of these 39 persons kissed
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,
must deduct 3 kisses.
We have, therefore, to deduct 42+171+3=216 kisses
from the above total of 861, and the result, 645,
number of kisses that were actually given under the mistletoe bough.