Problem:
At a twins and triplets convention, there were 9 sets of twins and 6 sets of triplets, all from different families. Each twin shook hands with all the twins except his/her sibling and with half the triplets. Each triplet shook hands with all the triplets except his/her siblings and with half the twins. How many handshakes took place?
Answer Choices:
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Solution:
Each of the 18 twins shook hands with 16 twins and 9 triplets, giving a total of handshakes. Similarly, each of the 18 triplets shook hands with 15 triplets and 9 twins, giving a total of handshakes. This tally counts every handshake twice, so the number of handshakes is .
The problems on this page are the property of the MAA's American Mathematics Competitions