# Combinatorial Mathematics - Puzzle

In one room of the science fair were six projects, and each project was entered by a pair of students. During the fair, some of the students visited other projects in the room and shook hands with some of the other project entrants. No students shook hands with their own partners. After the fair, the students discussed the project they have visited. Hannah learned that no two of the other eleven students had shaken the same number of hands. How many hands did Hannah's partner shake?

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#### Solution Preview

In one room of the science fair were six projects, and each project was entered by a pair of students. During the fair, some of the students visited other projects in the room and shook hands with some of the other project entrants. No students shook hands with their own partners. After the fair, the students ...

#### Solution Summary

The expert examines some combinatorial mathematics puzzles.