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Questions tagged [mathematics]

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

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

106 questions
28
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9 answers

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 to imagine that it should be possible to describe…
postoronnim
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28
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4 answers

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)?
Sharlotta Neimor
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23
votes
5 answers

Least number of moves to achieve a complete switchover of nonpawns in starting setup

[fen "RNBQKBNR/8/8/pppppppp/PPPPPPPP/8/8/rnbqkbnr w - - 0 1"] During a comp, my friend an I had a team kill and we decided to make this position(legally) before drawing. Then we continued to find more and more optimal ways of getting the position…
Ariana
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1 answer

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: The question is: How many such positions are…
Mike
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15
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3 answers

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 greater than 32 half-moves. There are 30 pieces to…
ericw31415
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14
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2 answers

If repetition loses, who wins KvK?

Suppose we're playing a version of chess where you lose if you repeat once an earlier position (position = arrangement of pieces + who's move it is). We're down to the wire, and we've just arrived at the position after the 30th capture, with only…
Laska
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14
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7 answers

Arrange 5 non-attacking knights on a 5x5 toroidal board

The celebrated British mathematician and lover of public transport, Simon Norton, passed in 2019. He was the subject of a wonderful biography. He was not a particular fan of chess, but here is a tiny gem due to him. How many ways are there to…
Laska
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13
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1 answer

Checkmate in ω² moves with finitely many pieces

The post Checkmate in ω moves? has inspired a lot of discussion and mathematical research into positions on an infinite chessboard where white can mate in a transfinite amount of moves. The current record for a game value of a position with finitely…
Andreas Tsevas
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12
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8 answers

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 be infinite? Source
Quaxton Hale
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12
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3 answers

How often do Super GMs achieve 100% engine correlation?

There has been speculation that anomalous values of a correlation metric1 may hint to the use of outside assistance. Example Examination of Hans Niemann vs Matthieu Cornette surprises: Hikaru Nakamura: this looked like a perfect game Yosha…
stevec
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12
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1 answer

Is the number of legal chess positions odd or even?

Is the number of legal chess positions odd or even? Two positions are not the same if they differ in castling rights (i.e. whether K or R have actually moved) or en passant capability (i.e. whether the move can actually be made) or who has the…
Laska
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5 answers

Approximating a rating for too strong engines

Suppose we have an extremely strong engine that happens to win every game it participates in even against the most powerful engines and players. If it continues to win every game, its rating (for example ELO) will grow indefinitely. But we do not…
DKozl
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3 answers

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 teacher): ... Assume that a game is played with the new rule…
Favst
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11
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3 answers

What is the average number of legal moves per turn?

For example in the first turn there are 20 possible legal moves (16 pawn moves and 4 knights moves). This number increases in the middlegame and then decreases in the Endgame. Are there some calculations on the average? Google search seem to be…
Superluminal
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Where can I find Pauls' 1874 article on the n-queens problem?

Where can I find the following article, which concerns the n-queens problem? E. Pauls, Das Maximalproblem der Damen auf dem Schachbrete, II, Deutsche Schachzeitung. Organ f¨ur das Gesammte Schachleben 29 (9)(1874) 257–267.
benedito
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