All Questions
10
questions
1
vote
1
answer
110
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Number of ways to place $4$ kings on an $n \times n$ chessboard
I have an $n \times n$ chessboard and $4$ kings on it. My goal is to count the number of arrangements where some of them are non-attacking or mutually attacking, for example:
In the case where the $4$...
- 159
0
votes
2
answers
144
views
A beetle on each square of a $9 \times 9$ chessboard. Each beetle crawls one square diagonally, find minimal possible no. of free squares.
Question:
A beetle sits on each square of a $9 \times 9$ board. At a signal each beetle
crawls diagonally onto a neighboring square. Then it may happen that
several beetles will sit on the same ...
- 5,316
3
votes
0
answers
145
views
Are there large $n$-queens solutions without 3-in-a-line?
Wikipedia references: N-queens & No-3-in-line
The 4-queens board is few enough pieces that it never has three queens on the same line
...
- 181
9
votes
5
answers
1k
views
How to calculate the number of paths of minimum length possible a knight can take to get from one corner of a chess board to the opposite one?
I've written a small Python script to give me the least number of moves it takes a knight to get from one square to any other on a $n{*}n$ chess board.
But then I've wondered how many paths the knight ...
- 243
1
vote
0
answers
72
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Number and Density of Possible Checkmates
Is there a way to estimate the number of possible checkmates on a chess board? By possible, I mean that it corresponds to some board state. If it's easier to estimate, I don't mind whether the number ...
- 31
2
votes
0
answers
112
views
Let $n \geq 3$. Take an $2n \times 2n$ chessboard, and remove $2$ white pieces and $2$ black pieces, can you always cover it with dominoes?
I am reading "Kombinatorika" by Laszlo Lovasz, Katalin Vesztergombi and Jozsef Pelikan(in Japanese, translated and arranged by Jin Akiyama and Peter Frankl).
There is the following problem ...
- 8,750
3
votes
1
answer
1k
views
Distance formula for generalized knight movement on infinite chessboard from a corner
Consider a chessboard infinite in positive x and y directions, all square has non-negative integer coordinates, and the only corner is at $(0,0)$. A $(p,q)$-knight is a piece that can move so that ...
- 814
10
votes
3
answers
1k
views
Independence problem: one rook and maximum number of knights on the chessboard $8 \times 8$
On the chessboard $8 \times 8$ we can to place one rook and several knights. Find the maximum number of knights, which can be placed on a chessboard along with one rook so that none of the pieces ...
- 952
0
votes
1
answer
1k
views
Maximum number of kings on the chessboard subject to some rules
The chess king moves one square in any direction (horizontally, vertically, or diagonally). The goal is to place as many king as possible on an r×c board subject to the following two conditions:
...
0
votes
3
answers
307
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the subtraction of numbers on chess board is at least 5.
assume we own a regular chess board (8 by 8), now we will randomly write in the slots of the board numbers from 1 to 64 (every number we will write exactly one time), show that the probability that {...
- 987