Solution – The last coin game

There is a winning strategy for the player who places the first coin. We will call him player 1.

To win every round, player 1 must:

1. Place the first coin in the center of the board.
2. In the second round, after player 2 makes his move, player 1 must place his coin in a symmetrical position to the other player’s coin.
3. Repeat the strategy every turn, until there are no spaces left to place the coins on the board.

In the picture below, we can see an example of a move of the winning strategy:

Player 1 placed the first coin at the center of the board, and after player 2’s turn, he will put the coin symmetrically to the position of player 2’s coin, in relation to the center. Player 1’s second position is shown by the transparent red circle.