Imagine a grid of squares, like a tic-tac-toe board, that goes on infinitely in all directions.

Players alternate taking turns marking the board with X's and O's. The winner is the first player to get four marks in a row (horizontally, vertically, or diagonally).

On each turn, a player may either:

A: Place two of his/her marks on the board, or

B: Remove one of the other player's marks, and then place one of their own.

With optimal play, does either player have a forced win, or will this game continue on infinitely?

of course it one could win, considering you could put 2 in each time. say you have three lined up in a row.

Ex. XXX

then say your opponent decides to block you. he has several ways of doing so.

OXXXO - using two of his pieces to cover one of your own

OXX - taking up one of your pieces and laying one of his pieces down.

XXO - again ^

now, that leaves with his turn over. then at your turn, you could easily beat him with each of these moves.

OXXXO= take up one of his pieces, and put one of your own, making it OXXXX or XXXXO

for the other two, one would simply place ones own pieces at the end which is open. thus the game is winnable. but this is assuming that the player could get themselves three in a row without any resistance from an opponent. say the games starts as follows:

Turn 1: XX

Turn 2: XXOO, XO, OOXX, OX

Turn 3: XXXXOO (a win) but what of the others?

Turn 3b: XO

Turn 4: XXXO (a win in two turns, as shown previously)

so in conclusion: one, using the right amount of logic and assuming the rules are typed correctly, could easily win at this game.

i think i got all this right >_>

 

Posted by dylan on 2007-01-30 12:59:09