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 $2 A$ is presented in the form of a sum of some natural numbers smaller than 10, $2 A = a_{1} + a_{2} + \dots + a_{k}$ , 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 $A$ .

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