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Results tagged with mathematics
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user 8201
Questions concerning the mathematics of the game of chess, or chess-related mathematical pursuits.
6
votes
Longest chess game possible (maximum moves)
The answer depends on preference:
If you apply a 50-move limit, the longest possible chess game is 5898.5 moves long.
If you apply a 75-move limit, it is 8848.5 moves long.
See https://wismuth.com/c …
- 13.6k
3
votes
How many different kinds of fairy leapers/riders can there be?
Just want to put in a partial solution to provide an independent count to validate other solutions.
Note that I take both zero & dummy to be legal units.
A couple of general points:
Take 0 =< p =< q
…
- 13.6k
41
votes
Accepted
Has anyone attempted to characterize chess mathematically?
A few books
There is also already a book "Mathematics and Chess" by Miodrag S. … A comment below mentioned "Games & Mathematics" by David Wells, which gives chess as an example of an abstract game, and also devotes a chapter to how chess is not mathematics. …
- 13.6k
2
votes
Is the number of legal chess positions odd or even?
Happy Halloween!
Basically the only possible approach to determining the parity of the number of positions is to pair off positions with one another, and then consider the remainder. The position afte …
- 13.6k
1
vote
Accepted
Longest sequence before a certain capture
Fun concept! I think you can at least retract a couple of moves from your extended example: R: 1. a5-a4 a2-a3 2. a6-a5 fxRg3 3. fxNe6 Nf8xRe6+
- 13.6k
10
votes
Accepted
Square Free Position
TL;DR: a solution!
[FEN "rnbq1bn1/p2pp1p1/1p2r1Nk/2p4p/6PN/1BPP1p1P/PP2PP2/R1BQK2R w - - 0 1"]
32 pieces, no squares.
According to OEIS sequence A240443 and this particular pair of examples, 34 is th …
- 13.6k
3
votes
Number of distinct checkmate positions
I haven’t come across this question before. I don’t have the time to execute it, but hope these remarks and suggested approach are helpful.
First let’s clarify:
(1) without loss of generality, white i …
- 13.6k
4
votes
Fastest King vs King endgame
Francois Labelle has studied this as part of the more challenging problem of finding a unique proof game which ends with KvK. Labelle's site contains a wealth of computational chess results, including …
- 13.6k
2
votes
Pal Benko's final problem
No answers here, and I haven’t seen any solution in the rest of the world. So I thought I would post a work-in-progress here.
First let’s take a baby step. Which player is the one who has all these a …
- 13.6k
6
votes
Which collections of pieces are legal?
Yes the characterization is correct, and there are 58,084,310 legal collections in total.
To make headway, we need the right level of discourse, avoiding loss of accuracy while avoiding diving into tr …
- 13.6k
1
vote
16 roses, 16x16 board; maximum double-attacked squares while all 256 squares are attacked at...
Sopel hasn't been around for a couple of years, but his solution is pretty and worth posting.
The pink squares contain the 16 roses. Each rose attacks all the squares whose distance away is sqrt(5), …
- 13.6k
3
votes
Accepted
Longest possible game of Horde Chess
EDIT: Final calculation matches actual proof game exactly.
That’s a nice new chess-math question, which deserves wider circulation.
Begin by promoting a White pawn as quickly as possible, because unti …
- 13.6k
7
votes
Arrange 5 non-attacking knights on a 5x5 toroidal board
(EDIT: substantially revised because I hadn't thought carefully enough about Rosie F's labeling. The result is even cooler!)
Thanks for all the great answers. I would like to add my own solution.
It's …
- 13.6k
3
votes
Accepted
If repetition loses, who wins KvK?
It's been long enough. Here's John's beautiful answer.
Suppose the Black king has just captured the 30th unit, to leave the two kings alone. White now chooses a 2x2 square currently containing the kin …
- 13.6k
16
votes
Accepted
When can legions of knights on an infinite chessboard checkmate a lone king?
If the king is at least three squares away from the infinite east-west line of knights then imagine the king starts running away to the north. At some point, after making n moves the king must be prev …
- 13.6k