MathDB

Odin and Evelyn are playing a game, Odin going first. There are initially

3k

empty boxes, for some given positive integer

k

. On each player’s turn, they can write a non-negative integer in an empty box, or erase a number in a box and replace it with a strictly smaller non-negative integer. However, Odin is only ever allowed to write odd numbers, and Evelyn is only allowed to write even numbers. The game ends when either one of the players cannot move, in which case the other player wins; or there are exactly

k

boxes with the number

0

, in which case Evelyn wins if all other boxes contain the number

1

, and Odin wins otherwise. Who has a winning strategy?

Agnijo \ Banerjee \ , United \ Kingdom

Problem Statement