MathDB

a_1,a_2,\ldots,a_n

is a sequence of positive integers that has at least

\frac {2n}{3}+1

distinct numbers and each positive integer has occurred at most three times in it. Prove that there exists a permutation

b_1,b_2,\ldots,b_n

a_i

's such that all the

n

sums

b_i+b_{i+1}

are distinct (

1\le i\le n

b_{n+1}\equiv b_1

)
Proposed by Mohsen Jamali

Problem Statement