MathDB

1

Part of the 16th XMO

Problems(1)

Tricky Algebra

Source: 16th XMO P1

6/20/2024
Let a1,a2,…,an≥0.a_1,a_2,\ldots ,a_n\ge 0. For all 1≤k≤n1\le k\le n define bk:=min⁡1≤i<j≤n,j−i≤2∣2ak−ai−aj∣.b_k:=\min_{1\le i<j\le n,j-i\le 2}|2a_k-a_i-a_j|. Here the index mod n.n. Find the maximum value of b1+b2+⋯+bna1+a2+⋯+an.\frac{b_1+b_2+\cdots +b_n}{a_1+a_2+\cdots +a_n}. Proposed by Zheng Wang
inequalities