# Circular Hand-holding

**Discrete Mathematics**Level 4

There are 6 people who are holding hands, such that each person is holding hands with exactly 2 other people. How many ways are there for them to do that?

**Details and assumptions**

Reflections count as distinct ways. Rotations count as the same way.

Each left hand grabs hold of a right hand.

A, B, C, D, E, F are arranged clockwise in a circle (with A at the 'top'), with A's left hand is holding on to B, so on and so forth. A reflection of this will be A, F, E, D, C, B are arranged clockwise in a circle (with A at the 'top'), with A's left hand holding on to F, so on and so forth. A rotation (of the first scenario) would be if C, D, E, F, A, B are arranged clockwise in a circle (with C at the 'top'), with C's left hand holding on to D, so on and so forth.

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