Alice and Bob move tile around a n-gon, who will win?
Source: Francophone 2024, Junior P2
April 4, 2024
combinatoricscombinatorics proposedgamewinning strategy
Problem Statement
Given points on a circle, Alice and Bob play the following game. Initially, a tile is placed on one of the points and no segment is drawn.
The players alternate in turns, with Alice to start. In a turn, a player moves the tile from its current position to one of the other points and draws the segment . This move is not allowed if the segment is already drawn. If a player cannot make a move, the game is over and the opponent wins.
Determine, for each , which of the two players has a winning strategy.