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?

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