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Tic-Tic-Tac-Tac-No-Toe

A new game for Xs and Os
Is played in four cols and four rows.
In Tic-Tic-Tac-Tac-No-Toe,
You must avoid 3-in-a-row.

This game is not very interesting. As in traditional Tic-Tac-Toe, all smartly played games should end in a tie. The person playing second in this game can successfully defend using symmetry as a strategy. How?

What is interesting is a puzzle based on this new game. There are exactly ten four-letter “safe words,” XXOX being an example. XXOX is a safe word since it avoids three-in-a-row for both players. List all ten “safe words,” then fill the grid so that all ten can be read in the rows, columns, and the two main diagonals.

Hint 1: Either letter can be placed in the upper left corner. Why?

Hint 2: If the grid were flipped diagonally along D1, nine words would be unchanged, so what must be true of the word in diagonal D2?

Source: Vaderland, Larson and Guy, The Inquisitive Problem Solver

Solution

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