Chosing any 10 (9) we can add 1 such a their sum is divisible by 10
Source: Assara 2024 J8
October 14, 2024
Setscombinatorics
Problem Statement
Given a set of natural numbers satisfying the following condition: if you select any (different) numbers from , then you can select another number from so that the sum of all selected numbers is divisible by . Prove that one of the numbers can be thrown out of so that the resulting set of numbers satisfies the condition: if you choose any (different) numbers from , then you can choose another number from so that the sum of all selected numbers is divisible by .
K.A.Sukhov