A chessboard is infinite such that for all positive integers x, y, there is a corresponding square (x,y). On this board, can a rook and king always beat a lone king if the player with the rook has the first move?Of course, the 50 move and 75 move rules are assumed not to apply here.Is this a classical problem? No, I don't think so.Is this a classic problem? No, I don't think so.Is this a well-known problem? Borderline. Many people have probably thought about it but the problem is too trivial for many people to find it interesting.CommodityQuant

Absolutely impossible. The only way to mate with a rook + king is to force the lone king to the back rank. By definition, you don't have a back rank here. Also, in chess, there is no such thing as 75 move rules. It's only 50 moves draw. You seem to have confused the chess rules!!!!

I think the answer is yes.First step, put the rook outside the opponent's king (outside means both x and y are superior)Second step, put your king outside the opponent's king. It's feasable because your king can move in diagonal (increase both x and y) and you can force his king not to increase both at the same time.Third step, classical one because it's a finite boardgame as your rook determines the 2 missing sides (always keep your king outside his one)

Ok. Can you please give me an example how to checkmate the king if the board is infinite and the lone king is on d4?

The board is infinite only on two directions, you have a corner.

Ok. I got it, I missed the part that the integers are positive, negative not included. I admit the answer is a simple yes. It's very simple if we have a corner.

QuoteOriginally posted by: studenttt Also, in chess, there is no such thing as 75 move rules. It's only 50 moves draw. You seem to have confused the chess rules!!!!studentt,Firstly, I think you have used far too few exclamation marks, thus not putting enough emphasis on your point. Surely you should have used more than 100 exclamation marks, rather than a mere 4. Secondly, please consult articles 9.3 and 9.6 the most recent FIDE handbook: http://www.fide.com/fide/handbook.html? ... ew=article. The 50 move rule states (roughly speaking) that a player can claim a draw after 50 moves with no capture or pawn move. However, this would be a voluntary action. There is nothing to stop both players continuing to try to win. However, there is another threshold of 75 moves. When 75 moves have been played with no capture or pawn move, the game is drawn whether the players like it or not.CommodityQuant