Board with squares

[samuel.bradley.99]

Alice and Bob have drawn a table with 11 columns x 10 rows and take turns to mark 1 to 3 squares at a time. Alice plays first and in each move she can mark squares only from one column, while Bob can mark squares from different columns, but at most one from each column. Each square can only be marked once. The player who marks the last square is the winner. If both players play perfectly, is there a winning strategy for any of the two? If yes, describe it!

 

[mmm4444bot]

Have you tried playing? If not, you could be both Alice and Bob, using a simpler version -- maybe four rows and five columns.

I can think of something that might work for Bob, to reduce Alice's options toward the end of the game. i can think of something that might work for Alice, too. I haven't played the game; I just focused on the fact that Alice is constrained to a single column per turn, while Bob is constrained to marking only one square per column.

I'm not sure what "play perfectly" means; it seems to suggest that there are strategies. :cool:

 

[samuel.bradley.99]

Have you tried playing? If not, you could be both Alice and Bob, using a simpler version -- maybe four rows and five columns.

I can think of something that might work for Bob, to reduce Alice's options toward the end of the game. i can think of something that might work for Alice, too. I haven't played the game; I just focused on the fact that Alice is constrained to a single column per turn, while Bob is constrained to marking only one square per column.

I'm not sure what "play perfectly" means; it seems to suggest that there are strategies. :cool:

I guess "playing perfectly" means that each player wouldn't make a move that would clearly "help" the opponent, or that he wouldn't deliberately loose some opportunity to win.
Usually in such problems we start from the end, with backward reasoning. That is, we must leave the opponent with 4 squares, so that he takes 1 or 2 or 3 and then we take 3 or 2 or 1 respectively, and win. But this would work only if Alice did not have the constraint to mark squares only from one column