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RU-SPB 2018 Problem 94

  • Grade 9

On the round necklace there are n>3n> 3 beads, each painted in red or blue. If a bead has adjacent beads painted the same color, it can be repainted (from red to blue or from blue to red). For what nn for any initial coloring of beads it is possible to make a necklace in which all beads are painted equally?

Dataset text AI-MO AoPS. Quoted with source.

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