[Guest]

(I'm couldn't find this puzzle when searching. Forgive me if this has been posted before.)

There is one solitary king on a1. Players take turns moving the king. The king can only go up, to the right, or diagonally up-right. The player who gets the king to h8 wins.

Is there a winning strategy? If so, who will always win with what strategy?

[Guest]

The solitary king moves from A1 to H8 in 8 easy diagonal steps. What is the problem here? On the face of it it is trivial.

[Guest]

Without looking at it mathematically, and assuming there are 2 players, it would seem that if player one manages to ensure that an odd number of diagonal moves are made, then he will win. I havent examined the options sufficiently to see whether this is possible in all game situations

[Guest]

(I'm couldn't find this puzzle when searching. Forgive me if this has been posted before.)

There is one solitary king on a1. Players take turns moving the king. The king can only go up, to the right, or diagonally up-right. The player who gets the king to h8 wins.

Is there a winning strategy? If so, who will always win with what strategy?

there is no winning strategy...anyone can win the match...everyone will try and push the other to move to cell H7/G7/G8..and once any1 reached there its game over for them!! until then there are n permutations!

[witzar]

The player who moves first has a winning strategy:

his first move is made diagonally, then he keeps repeating his opponent's moves (if his opponent moves right, he moves right, etc.).

[witzar]

The player who moves first has a winning strategy:

his first move is made diagonally, then he keeps repeating his opponent's moves (if his opponent moves right, he moves right, etc.).

Why this works? Suppose chessboard squares have horizontal and diagonal coordinates ranging from 1 to 8, so that the Kings starts at square (1,1) and finishes at square (8,8). Observe that the above strategy ensures, that after every move of the first player the King is on the square with both coordinates being even numbers, and every move of his opponent the King is on the square with at least one coordinate being odd. The final square of the King journey (8,8) has both coordinates even, so only the first player can get there.

[araver]

@witzar

Adding a visual representation to what you just said (which is correct IMO)

1 and 2 are player moves according to witzar's strategy:

X 1 2 1 2 1 2 1

X 2 2 2 2 2 2 2

X 1 2 1 2 1 2 1

X 2 2 2 2 2 2 2

X 1 2 1 2 1 2 1

X 2 2 2 2 2 2 2

X 1 2 1 2 1 2 1

X X X X X X X X