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Necklace problem
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== Upper bounds == [[Noga Alon|Alon]], [[Yair Caro|Caro]], [[Ilia Krasikov|Krasikov]] and [[Yehuda Roditty|Roditty]] showed that 1 + log<sub>2</sub>(''n'') is sufficient, using a cleverly enhanced [[inclusion–exclusion principle]]. [[Jamie Radcliffe|Radcliffe]] and Scott showed that if ''n'' is prime, 3 is sufficient, and for any ''n'', 9 times the number of prime factors of ''n'' is sufficient. Pebody showed that for any ''n'', 6 is sufficient and, in a followup paper, that for odd ''n'', 4 is sufficient. He conjectured that 4 is again sufficient for even ''n'' greater than 10, but this remains unproven.
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