New answers tagged mathematics
2
It is true that for larger numbers of moves it becomes easier. From the following solutions, the ones from n=2 to n=8 are clearly optimal. The solution for n=1 looks good, but it may not be optimal.
All pieces have 1 move
[FEN "8/8/8/1pp5/8/K7/8/k7 w - - 0 1"]
2 moves (found by ghilesZ)
[FEN "2k5/K1p5/8/8/8/8/8/8 w - - 0 1"]
3 moves
[...
3
The minimum number of knight moves required to be able to reach every square on the board, is 4 to 6, depending on which square you start from. Below is an overview; the number in each square indicates the minimum number of moves when starting from that square:
[6,5,5,5,5,5,5,6]
[5,5,5,4,4,5,5,5]
[5,5,4,4,4,4,5,5]
[5,4,4,4,4,4,4,5]
[5,4,4,4,4,4,4,5]
[5,5,4,...
13
You are asking for the diameter of the knight's graph. I suppose you only want it for the ordinary 8x8 chessboard. (See OEIS sequence A232007 for diameters of knight's graphs on square boards of size nxn, in particular confirming my answer 6 for the case n = 8. The answer is alleged to be ceiling(2n/3) for n > 4.)
The answer is 6. It takes 6 moves to get ...
2
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 is mating black
(2) position must be legal - in particularly white king must be on the board even if it doesn’t otherwise contribute to the mate.
(3) ...
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