2024 SSMO Relay Round 1 Problems/Problem 2

Problem

Let A circular necklace is called if it has black beads and white beads. A move consists of cutting out a segment of consecutive beads and reattaching it in reverse. It is possible to change any necklace into any other necklace using at most moves. Find . (Note: Rotations and reflections of a necklace are considered the same necklace).

Solution

Every time we reverse a section, we can "fix" the position of at least one bead. When only two beads are out of place, we can "fix" their positions with only one move. So, the answer is Since we have

~SMO_Team