# Time Bomb

$$n$$ people stand in a circle. One is given a ticking bomb with $$n-1$$ seconds left. The bomb is then thrown around the circle every second in an orderly, mathematical fashion; when the bomb has $$k$$ seconds left, it is thrown to the person $$k$$ places clockwise. Determine the sum of all values of $$n$$ with $$1 \le n \le 100$$ for which each person holds the bomb exactly once.

×