# Puzzle 80 | Tic Tac Toe revisited

Ank and Mini play a game of tick-tack-toe. In this game, the players try to get three circles or three crosses in a row (horizontal, vertical, or diagonal).

They follow the following rules:

- A player always tries to win: if a player can place his own symbol (X or O) in a row that already contains two of his own symbols, he will do so.
- A player always tries to avoid that his opponent wins: if a player can place his own symbol (X or O) in a row that already contains two of the symbols of his opponent, he will do so.

Of course, the first rule has precedence over the second rule, because the game can be won in this way.

In the game shown on the right, six moves have been made. Ank plays with crosses (X) and Mini plays with circles (0). However, we do not know who started the game. **Who will win the game?**

**Solution:**

It is clear that if we know who made the sixth move, we also know who can make the seventh move and wins. If Mini (circles) has made the sixth move, there are three possibilities for the situation after five moves:

Based on the rules of the game, only possibility 1 could have resulted in the situation after six moves. In that case, there are three possibilities for the situation after four moves:

Based on the rules of the game, Ank (crosses) would have made the winning move, which however did not happen. From this, we can conclude that Ank did not make the fifth move and Mini did not make the sixth move. Therefore, Ank must have made the sixth move and Mini can make the seventh, winning move!

To check that Ank could indeed have made the sixth move, we look at the following three possibilities after five moves:

Based on the rules of the game, only possibility 3 can result in the situation after six moves. Therefore, Ank could indeed have made the sixth move.

**Conclusion:** Ank has made the sixth move, and Mini will make the seventh move and win.

You may also like – Tic Tac Toe

This puzzle is contributed by **Praveer Satyam**. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

## Recommended Posts:

- Puzzle 1 | (How to Measure 45 minutes using two identical wires?)
- Puzzle 2 | (Find ages of daughters)
- Puzzle 3 | (Calculate total distance travelled by bee)
- Puzzle 4 | (Pay an employee using a 7 units gold rod?)
- Puzzle 13 | (100 Prisoners with Red/Black Hats)
- Puzzle 5 | (Finding the Injection for Anesthesia)
- Puzzle 6 | (Monty Hall problem)
- Puzzle 7 | (3 Bulbs and 3 Switches)
- Puzzle 8 | (Find the Jar with contaminated pills)
- Puzzle 9 | (Find the fastest 3 horses)
- Puzzle 10 | (A Man with Medical Condition and 2 Pills)
- Puzzle 11 | (1000 Coins and 10 Bags)
- Puzzle 12 | (Maximize probability of White Ball)
- Puzzle 14 | (Strategy for a 2 Player Coin Game)
- Puzzle 15 | (Camel and Banana Puzzle)