MathDB

Let

n\geqslant 3

be a positive integer. A circular necklace is called fun if it has

n{}

black beads and

n{}

white beads. A move consists of cutting out a segment of consecutive beads and reattaching it in reverse. Prove that it is possible to change any fun necklace into any other fun necklace using at most

(n-1)

moves.
Note: Necklaces related by rotations or reflections are considered to be the same.
Proposed by Dylan Toh

Problem Statement