All Questions
Tagged with checkmate mathematics
10 questions
11
votes
2
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3k
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When can legions of knights on an infinite chessboard checkmate a lone king?
On an infinite (perhaps only in one direction?) chessboard, what kind of configuration of (possibly a very large number of) knights could checkmate a lone king? I'm really thinking of an infinite-in-...
- 335
15
votes
1
answer
3k
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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 ...
- 541
3
votes
1
answer
302
views
Mate-in-N problems where N scales indefinitely with board size
Motivation - Long range mating patterns
This question is inspired by my recent interest in infinite chess and the post on MathOverflow Checkmate in ω moves?. Since my chess endgame skills are quite ...
- 541
4
votes
1
answer
435
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Number of distinct checkmate positions
What is the number of distinct checkmate positions in each of the following categories given the following conditions?
We are not interested in whether the position can be forced or not or even what ...
11
votes
3
answers
2k
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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 ...
- 221
-4
votes
1
answer
223
views
What is the total number of KNN vs K checkmate positions?
What is the total number of KNN vs. K checkmate positions? Assume that White is checkmating.
Firstly the Black king must be mated on a corner. It is impossible to do it on the edge. The calculations ...
- 17.8k
2
votes
2
answers
353
views
How many two move checkmates exist?
I am well aware that Fool's Mate exists. But how many two move checkmates exist in total?
- 17.8k
4
votes
3
answers
401
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Knights necessary to mate king on large finite board
How many knights would be necessary to mate opponent's king on large finite boards, like a billion times a billion squares?
Are they fast enough to surround the opponent's king in a constant number of ...
- 3,286
6
votes
1
answer
778
views
Checkmating with two bishops
Let White have the two bishops. Given any setup, has the maximum number of moves to forced mate been calculated on an nxn board (for large enough n)? If not, are there any bounds on this number?
Of ...
- 607
19
votes
1
answer
2k
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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:
...
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