Xander and Olivia are playing a three-game tic tac toe match.
Each game is worth one point, which is either earned by the winner or split if a game ends in a draw.
To make the match more interesting, they're playing all three games at once -- that is,
on each turn a player may put his or her initial into any empty box in any of the three gameboards.
Xander goes first. After two turns by each player, the boards look like this:
Where should Xander play next to be sure of winning the match?
Click here for an analysis of the game of Tic Tac Toe
Solution to the Problem:
To analyze the situation, consider what will happen if X plays first, then consider what will happen if O plays first, in each of the three games.In the left-hand game, an X play (anywhere) will lead to a win even against a perfect defense, but an O play (in the center) will result in a draw with best play by both sides.
In the center game, X can draw by going first (in a corner), while O going first (anywhere) will win.
In the right-hand game, whoever goes first (by playing in the center) will win, and so that's where Xander should play.
The other two games will then cancel each other out: if O defends on the first board, X will defend on the second board; while if O plays on the second board and wins it, X will play on and win the first board. Either way, X comes out on top 2 - 1.
Correctly solved by:
| 1. James Alarie | Flint, Michigan |