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numbers in circle, circular arc with sum s, 1<= s <= 1/2 n(n+1)

Source: INAMO Shortlist 2014 C6

July 13, 2019
combinatoricscirclearc

Problem Statement

Determine all natural numbers nn so that numbers 1,2,...,n1, 2,... , n can be placed on the circumference of a circle and for each natural number ss with 1≤s≤12n(n+1)1\le s \le \frac12n(n+1) , there is a circular arc which has the sum of all numbers in that arc to be ss.
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