Adding and multiplying numbers on the board
Source: Macedonian TST 2022, P6
May 21, 2022
combinatorics
Problem Statement
The numbers 1, 2 and 3 are written on a board. Two friends are playing the following game. A player writes a number that doesn't exceed 2022 and isn't already on the board and is a sum or a product of two numbers that are written on the board. They take turns writing numbers and the winner is the player who writes 2022 on the board.
Which player has a winning strategy and why?Proposed by Ilija Jovcheski