1. ## Chessboard Problem!

Suppose a queen starts out standing on the third square on a chessboard at the very top. That is, the queen stands on the 3rd sqaure from the left. Two players play a game where each player takes a turn moving the queen:

a.) either horizontally to the right
b.) or vertically downward
c.) or diagonally in south-east direction

For the above, they can move the queen as many squares as they want.

The first player that can place the queen on the lower-left most right square of the chessboard wins the game.

Who will win, and what is the winning strategy for each n and m?

2. Any suggestions on where to even start or how to approach this question? How do you suggest trying to come up with an equation that works in general? Different cases?

3. Originally Posted by fifthrapiers
Suppose a queen starts out standing on the third square on a chessboard at the very top. That is, the queen stands on the 3rd sqaure from the left. Two players play a game where each player takes a turn moving the queen:

a.) either horizontally to the right
b.) or vertically downward
c.) or diagonally in south-east direction

For the above, they can move the queen as many squares as they want.

The first player that can place the queen on the lower-left most right square of the chessboard wins the game.

Who will win, and what is the winning strategy for each n and m?
Lower left most right square?

What n and m? Do youmean an n by m board rather than the standard board.

4. "The first player that can place the queen on the lower-left most right square of the chessboard wins the game.

Who will win, and what is the winning strategy for each n and m?"

Err, sorry. I meant the first player that can place the queen on the lower-right most square (IE: bottom right corner) of the chessboard wins.

"What n and m? Do youmean an n by m board rather than the standard board."

Yes.

5. "What n and m? Do youmean an n by m board rather than the standard board."

Nevermind on that. I misread the question. It's just "what is the winning strategy." No n's or m's.

6. Originally Posted by fifthrapiers
Suppose a queen starts out standing on the third square on a chessboard at the very top. That is, the queen stands on the 3rd sqaure from the left. Two players play a game where each player takes a turn moving the queen:

a.) either horizontally to the right
b.) or vertically downward
c.) or diagonally in south-east direction

For the above, they can move the queen as many squares as they want.

The first player that can place the queen on the lower-left most right square of the chessboard wins the game.

Who will win, and what is the winning strategy for each n and m?
Similarly to analyzing the game in this thread, analyze the game backwards from last move.

Form the board, which is effectively 8x6 because the queen cannot move to the left. See below. Starting from the lower right corner, mark a position as W for winning if a player can win outright from there or put the opponent into a losing position. Mark a position as L for losing if the player is forced to put the opponent into a winning position. Q denotes where the queen starts. X is the final position. A winning strategy is to move to one of the L positions reachable from Q.

Code:
QLWWWW
WWWWWW
WWLWWW
WWWWWW
LWWWWW
WWWWLW
WWWLWW
WWWWWX