2player game, adding numbers, whoever reaches no >= 2019 wins
Source: 2019 Austrian Mathematical Olympiad Junior Regional Competition , Problem 3
December 18, 2020
combinatoricsgamegame strategyAustria
Problem Statement
Alice and Bob are playing a year number game.
There will be two game numbers and and one starting number from the set used. Alice chooses independently her game number and Bob chooses the starting number. The other number is given to Bob. Then Alice adds her game number to the starting number, Bob adds his game number to the result, Alice adds her number of games to the result, etc. The game continues until the number is reached or exceeded.
Whoever reaches the number wins. If is exceeded, the game ends in a draw.
Show that Bob cannot win.
What starting number does Bob have to choose to prevent Alice from winning?(Richard Henner)