MathDB

2

Part of 2021 Greece Junior Math Olympiad

Problems(1)

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)

7/3/2021
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 nn, the player whose turn is chooses a prime divisor pp of nn and writes the numbers n+pn+p. In the board, is written at the start number 22 and Anna plays first. The game is won by whom who shall be first able to write a number bigger or equal to 3131. 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.
gamegame strategycombinatoricswinning strategyprime divisor