MathDB
we can select from a_1, a_2,..., a_k some numbers so that sum of these is S

Source: 2015 Saudi Arabia IMO TST III p1

July 24, 2020
combinatoricsSum

Problem Statement

Let SS be a positive integer divisible by all the integers 1,2,...,20151, 2,...,2015 and a1,a2,...,aka_1, a_2,..., a_k numbers in {1,2,...,2015}\{1, 2,...,2015\} such that 2S≤a1+a2+...+ak2S \le a_1 + a_2 + ... + a_k. Prove that we can select from a1,a2,...,aka_1, a_2,..., a_k some numbers so that the sum of these selected numbers is equal to SS.
Lê Anh Vinh
Back to ProblemsView on AoPS