Questions tagged [mathematics]

Questions concerning the mathematics of the game of chess, or chess-related mathematical pursuits.

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8
votes
3answers
3k views

What is the number of legal positions in a chess game?

There have been several questions regarding the possible number of chess games. for example; Database of every possible move in chess. However,can there be an estimate on the number of "allowable&...
13
votes
3answers
485 views

Fastest King vs King endgame

What is the fastest possible game that ends in a King vs King endgame? Please post a game and tell me the number of half-moves you've achieved. By some simple logic, I can prove that this number is ...
25
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8answers
15k views

Has anyone attempted to characterize chess mathematically?

From years of being student, researcher, and practitioner of chess, I feel like it possesses completeness and elegance that are found in mathematical proofs and theories. Thus, it seems only natural ...
27
votes
4answers
7k views

Stalemate situation with all pieces on the board

Suppose all the pieces are on the board. Does there exist a position such that A) one of the players can't make any move (a stalemate)? B) neither player can make any move (a double stalemate)?
7
votes
3answers
1k views

Of all the possible legal chess games, how many end in white win, draw and black win (assuming 50 move rule)?

If both sides make moves completely randomly but legally, how many different games are there? Since the 50 move rule applies, this number should be finite (but HUGE). For example, there are 20 ...
3
votes
2answers
370 views

How many different knight's tours are there?

How many solutions does the Knight’s Tour puzzle have when the knight first moves from square a1, through all squares (on each square once), and return back to a1? Please give some solutions. Also, ...
18
votes
1answer
2k views

How many such positions are there? (chess/math checkmate puzzle)

I'm interested in this kind of position: There are only 4 pieces on the board. If Whites goes first, they can checkmate in one move. If Blacks goes first, they can checkmate in one move. For example: ...
4
votes
3answers
460 views

Puzzles that highlight the finiteness of the chessboard

I'm curious as to whether there are compositions of chess puzzles/problems where the solution really emphasizes the boundedness of the board. Put differently, cases where the solution would be ...
1
vote
1answer
261 views

How many Chess960 positions exist in which castling on 1 side does not require moving the rook on the other side?

Update: It's chess870 (or chess869). See answer. Context/Motivation/Goal: In regular chess, you never have to move a rook (on 1 side) to castle (on the other side). My aim is to see how much of 9LX ...
13
votes
8answers
15k views

Longest chess game possible (maximum moves)

What is the longest chess game possible in terms of chess moves? I read somewhere that there is a theoretical maximum of 5949 moves. But I don't see any proof and I don't think it is correct. Can it ...
11
votes
3answers
2k views

How to solve this puzzle of Martin Gardner?

Martin Gardner mentioned the following "chess" problem in his column, Mathematical Games, for Scientific American (he got it from Smullyan, who learned about it from a high school math ...
7
votes
3answers
1k views

Longest Sequence For Any Piece To Reach A Certain Square

What is the longest sequence of moves (by both White and Black) wherein White attempts to move one of their pieces from one square to another? Assume Black makes every move optimal towards the purpose ...
6
votes
1answer
226 views

A New Year's Math Riddle

Here's a fun and clean riddle for the New Year! I found the material for it on Krabbe's site. I will provide the link when it is solved. How many times can this position be repeated, with both sides ...
5
votes
2answers
2k views

Chess480: Why 480?

From wiki: Lewis has named this chess variation "Chess480"; it follows the rules of Chess960 with the exception of the castling rules. Although a Chess480 game can start with any of 960 ...
4
votes
3answers
1k views

How does Elo rating gain scale with games played?

I only take two players starting out at 1500 Elo and have them play against each other with one player winning all games. Also I leave out any artificially introduced cut-offs. So the winner is ...
4
votes
2answers
2k views

How many times can the same pawn move be made in a game?

How many times in a game can "the same pawn move" be made? By "the same pawn move", I mean, a move made by a pawn that would be notated the same way. For instance, after 1.e4 e5 2....
4
votes
1answer
482 views

Minimal number of moves before castling in Chess960

As you know, in the initial position Chess960 the king lies between the two rooks. Here are the rules for castling. For a starting position P, let n(P) be the minimal number of moves that White needs ...
3
votes
1answer
125 views

A mobility puzzle

[FEN "8/8/8/8/pp6/kp6/1p6/1K6 w KQkq - 0 1"] This is a well-known position: both sides are stalemated (if it's their move). It's the lightest position with this property. Devise the ...
1
vote
1answer
63 views

How many unoriginal pawn moves can be made in a single game?

Consider an "unoriginal pawn move" to be a pawn move whose notation matches a move already played in the game. For instance, after 1.e4 e5 2.d4 exd5 3.e5, there is one unoriginal pawn move, ...