Difference between revisions of "2024 SSMO Relay Round 1 Problems/Problem 2"
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| + | 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 <math>2T-1.</math> Since <math>T = 360,</math> we have <math>2T-1 = \boxed{719}.</math> | ||
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| + | ~SMO_Team | ||
Latest revision as of 14:43, 10 September 2025
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
