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Tagged with puzzles mathematics
9 questions
19
votes
1
answer
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:
...
- 293
11
votes
3
answers
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 ...
- 221
7
votes
3
answers
1k
views
Square Free Position
[FEN ""]
For the purposes of this question, a “square” is a set of four occupied cells on the chessboard whose centres form a geometric square. The cell may have any orientation. For ...
- 325
4
votes
3
answers
402
views
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
4
votes
1
answer
165
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 ...
- 17.3k
3
votes
1
answer
188
views
How often can the initial position be repeated under FIDE tournament rules?
Recently a game was played where two GMs swapped kingside and queenside knights and then agreed a draw (and got their just dessert): How often can the starting position be repeated in a game without ...
- 17.3k
3
votes
1
answer
144
views
"Every" move in long notation
A move here shall be defined as the FIDE super-long notation of a legal chess move: Sg1-f3, O-O, e5xd6 ep, Da8xg8+, Rd1-d6# and whatnot. I.e. starting square, ending square, capture sign, check sign, ...
- 17.3k
3
votes
0
answers
46
views
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....
- 1,003
2
votes
2
answers
761
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, ...
- 543