MathDB

Two friends

A

and

B

must solve the following puzzle. Each of them receives a number from the set

\{1,2,…,250\}

, but they don’t see the number that the other received. The objective of each friend is to discover the other friend’s number. The procedure is as follows: each friend, by turns, announces various not necessarily distinct positive integers: first

A

says a number, then

B

says one,

A

says a number again, etc., in such a way that the sum of all the numbers said is

20

. Demonstrate that there exists a strategy that

A

and

B

have previously agreed on such that they can reach the objective, no matter which number each one received at the beginning of the puzzle.

Problem Statement