C6

Part of 2014 Indonesia MO Shortlist

Problems(1)

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

Source: INAMO Shortlist 2014 C6

Determine all natural numbers

n

so that numbers

1, 2,... , n

can be placed on the circumference of a circle and for each natural number

s

1\le s \le \frac12n(n+1)

, there is a circular arc which has the sum of all numbers in that arc to be

s

combinatoricscirclearc