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MathNet 2014 Question 51

Math Olympiad Vault · MathNet 2014

Question 51

Can the numbers $0,1,2,\ldots,9$ be arranged on a circle so that the sum of any three successive numbers is at most
(a) $13$, (b) $14$, (c) $15$?

Question illustration

Ten blank slots on a circle; no arrangement is prescribed.