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#1

One more

Dan Donaldson

Bill and Alex 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 which 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 which 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, 6 moves have been done. Bill plays with crosses (X) and Alex plays with circles (0). However, we don't know who started the game.

The Question: Who will win this game?


Re: One more

#2

I concede


Re: One more

#3

Re: One more

Larry Barrett

I think Alex wins, but clearly not the best efforts by either player.

Re: One more

#4

You can work it out

Dan Donaldson

Go backwards in time and look at the possibilities with the rules applied.

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#5

Re: You can work it out

Alex Y

I did. That's why I conceded. Bill went first, and will win.

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#6

Re: You can work it out

Dan Donaldson

I see you as winning.

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#7



Dan Donaldson

Agree about not being the best game. Not sure how they would ever get there if they knew how to play. If I go first, either I will win or no one will. and vice versa.

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#8

Re: You can work it out

Alex Y

Yeah, I went back one step and jumped to an unwarranted conclusion. :(

For Bill to win, that would mean my last move was to block him when the board was

0 _ _

0 X _

X X _

But that would mean his last move was to block me when the board was

0 _ _

0 X _

_ X _

But he wouldn't do that; he would just win.

I think the game went something like this:

0(5) 0(1) _

0(3) X(4) _

X(6) X(2) _

Not stellar tic-tac-toe play, as you and Larry point out.

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