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 kiss.
making a list of the
company, we can leave out the widower altogether,
because he took no part in the osculatory exercise.
||Bachelors and Boys
||Maidens and Girls
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, represents exactly
number of kisses that were actually given under the mistletoe bough.