2 player game, n-> n+p, where p is prime divisor of n
Source: 2021 Greek Junior MO p2 (served as Greek JBMO TST p2 since the latter didn't take place)
July 3, 2021
gamegame strategycombinatoricswinning strategyprime divisor
Problem Statement
Anna and Basilis play a game writing numbers on a board as follows:
The two players play in turns and if in the board is written the positive integer , the player whose turn is chooses a prime divisor of and writes the numbers . In the board, is written at the start number and Anna plays first. The game is won by whom who shall be first able to write a number bigger or equal to .
Find who player has a winning strategy, that is who may writing the appropriate numbers may win the game no matter how the other player plays.