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        riddles >> hard >> Tic-Tac-Toe with a twist
        
(Message started by: Mayank on Oct 18^th, 2004, 1:42pm)

Title: Tic-Tac-Toe with a twist
Post by Mayank on Oct 18^th, 2004, 1:42pm

You have a 3x3 matrix as in Tic-Tac-Toe. You can place 1 and 0 in it. There are two players involved.

Lets say, 'A' to 'I' represent the Matrix as mentioned below.

A B C
D E F
G H I

Lets assume the two players are M and N

Now Player M owns triangle created by ADGHIE and Player N owns triangle created by ABCFIE.

They have to play this game by putting 1 and 0 alternately on positions A, B, C, D and so on till I.

Their aim is not to have three 1's or 0's as in Tic-tac-toe, but to ensure that the sum of the sides of their respective triangle is same for all sides. For example.

0 1 1
1 1 0
0 0 1

Sum of the sides for Player M is: ADG = 1, AEI = 2, GHI = 1

While sum of the sides for Player N is: ABC = 2, AEI = 2, CFI = 2.

Hence player N will win in this example.

Please remember that the primary aim for both the players is getting the totals to match (for the win) and the secondary aim is to not to let the other player win. However this applies to all positions but the last i.e. "I". For the last move, the player's only aim is to get the total correct and the secondary aim is not valid. Infact, if he cannot win, and the other player can win, he has to let the other player win. Consider the above example, it is pretty clear that M cannot win and can avoid losing by putting a '0' in 'I', but he cannot do that and has to put a '1'.

Keeping all the above in mind:

1. What is the best sequence of moves that maximises the chances of winning for either player. Think about the best moves as per the current position on the matrix, as in best move for M on position 'A' then according to this move, what is the best move for N on position 'B' and so on.

2. Who has more chances of winning.