Problem #PRU-78234

Problems Methods Pigeonhole principle Algebraic methods Processes and operations

Problem

The number \(A\) is divisible by \(1, 2, 3, \dots , 9\). Prove that if \(2A\) is presented in the form of a sum of some natural numbers smaller than 10, \(2A= a_1 +a_2 +\dots +a_k\), then we can always choose some of the numbers \(a_1, a_2, \dots , a_k\) so that the sum of the chosen numbers is equal to \(A\).