Problem #40: Summit Meeting
Two delegations are to meet at the top floor of a skyscraper whose elevators
can hold up to nine people at a time. The first delegation to arrive makes up
a certain number of elevator loads, filling each one except the last, which
has space for five more people. The second delegation does the same, not using
one-third of the last elevator load.
At the start of the meeting, each member of each delegation shakes hands with
each member of the other delegation, and each time, a photo is taken. Knowing
that the photographer was using films with nine exposures on each, how many
unexposed frames will he have left on his last film?