A game on a hexagonal lattice
Source: Baltic Way 2018, Problem 9
November 6, 2018
geometryrhombus
Problem Statement
Olga and Sasha play a game on an infinite hexagonal grid. They take turns in placing a stone on a free hexagon of their choice. Olga starts the game. Just before the th stone is placed, a new rule comes into play. A stone may now be placed only on those free hexagons having at least two occupied neighbors.
A player loses when she or he either is unable to make a move, or makes a move such that a pattern of the rhomboid shape as shown (rotated in any possible way) appears. Determine which player, if any, possesses a winning strategy.