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2024 SSMO Relay Round 1 Problems/Problem 2

Revision as of 16:01, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>T = TNYWR.</math> A circular necklace is called <math>interesting</math> if it has <math>T</math> black beads and <math>T</math> white beads. A move con...")
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Problem

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

Solution

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