MathDB

2.

Part of 2023 Polish Junior MO Second Round

Problems(1)

Two integers on the board

Source: Polish Junior Math Olympiad 2023 Second Stage

5/14/2023
Initially, the numbers 22 and 55 are written on the board. A \emph{move} consists of replacing one of the two numbers on the board with their sum. Is it possible to obtain (in a finite numer of moves) a situation in which the two integers written on the board are consecutive? Justify your answer.
combinatorics