1)Take any 7, and take any 7.

2)Weigh them.

a)If equal then the remaining coin is lighter.

b)If unequal take the lighter one.

3)Spilt 3 with 3.

a)If equal then remaining coin is lighter.

b)If unequal take the lighter one.

4)Split 1 with 1

a)If equal the remaining coin is lighter.

b)If unequal take the lighter coin as the solution.

The worst case is 3 weighings.

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Does anybody know how to do this problem with math?

Looks like a graph theory problem, but I do not know.