All Questions
Tagged with mathematics problems
37
questions
3
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0
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40
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Maximum saved moves to win caused by zugzwang
For a zugzwang where x>y and:
If white has the move, White can force checkmate in x full moves
If Black has the move, White can force checkmate in y full moves
The score of such a zugzwang is x-y....
- 796
10
votes
2
answers
3k
views
Can a unique position be deduced if pieces are replaced by checkers (can see piece color but not type)
Inspired by a video where top players guess which famous game a position is from, except pieces in the position are replaced by checker pieces (so they can see the piece color but not type). Of course ...
- 592
3
votes
2
answers
2k
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Longest checkmates in (almost) fully covered boards?
What are the longest checkmates from initial positions which are (almost) fully covered in pieces? Down below I'll give examples of what I mean. An almost fully covered position can't be legal, ...
- 99
5
votes
1
answer
250
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Longest checkmates with the biggest material disadvantages in "open" positions?
We can ask a question:
What are the longest checkmates with the biggest material disadvantages? What, approximately, is the function between length of the checkmate and possible size of the material ...
- 99
14
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 ...
- 503
3
votes
1
answer
277
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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 ...
- 503
-1
votes
1
answer
75
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Longest sequence of moves where White's number of available moves does not change
There are challenges for the longest sequence of moves in which white's available moves increase or decrease. This challenge is for the longest sequence of moves (from the opening position) in which ...
- 3,340
2
votes
0
answers
97
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What is the longest sequence of increasing White moves with only White pieces?
Inspired by a comment by @Evargalo on this question, I ponder how long a sequence can last where each turn, White has more available moves than the previous turn, in a situation with only White pieces ...
- 17.7k
2
votes
1
answer
67
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Is there a Chess 960 position in which White's moves can be decreased to zero without check?
Inspired by this question, koedem proved that, from the starting position, White's legal move amount can be decreased sequentially from 20 to 0 in 20 moves. However, doing so required some checks. I ...
- 17.7k
6
votes
4
answers
637
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Longest sequence of moves where white's number of available moves decreases
An easier version of this
White has 20 available moves at the start of the game (from the standard position). After 1.h3 h5, white has 19 available moves. (The h pawn has lost the ability to move two ...
- 3,340
6
votes
3
answers
253
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Longest sequence of moves where number of available moves increases
White has 20 available moves at the start of the game. After 1.a4 e5, white has 21 available moves. (The rook has gained 2 moves, while the pawn has lost 1).
What is the longest sequence of moves ...
- 3,340
1
vote
1
answer
100
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Roundtrips with no shortcuts
In the picture, you see the longest roundtrip of a rook such that there are no "shortcuts" - imagine the target squares are given, then at each square you have exactly two other given ...
- 16.8k
11
votes
1
answer
449
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Open problems in chess involving maximum material imbalances
I am posting the present question since here Very unbalanced Chess Positions I have introduced three open problems (i.e., the third one, the fourth one, and the sixth one from the above), regarding ...
- 261
5
votes
2
answers
189
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How many more squares can you attack?
(Inspired by this cool problem)
Let’s say it’s White to move. Let A = the number of squares currently attacked by White, and B = the number of squares attacked by White after White’s next move.
What ...
- 241
2
votes
2
answers
264
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Fastest algorithm to give mate with K+R vs K on infinite large board as function of starting position
Consider a board with only two edges that are perpendicular.
Something like:
.------------------------------------------------------
| ^
| ...
- 355