66
votes
Accepted
57
votes
Accepted
53
votes
How can 3 queens control the white squares?
I think this arrangement works for the bonus question:
- 1,713
48
votes
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39
votes
Accepted
38
votes
Accepted
36
votes
Accepted
Dominos on a checkerboard
Looks like:
Thanks to @Gamow's comment, this number's maximality can be proved
by self-contradiction of the assumption that it is not maximal.
Any more dominos would cover all 64 squares.
Assumption ...
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36
votes
34
votes
Two Knights, two Bishops, two Rooks and two Kings on a 4x4 chessboard
I'm not trying to solve the puzzle, I'm just interested in how many solutions there are, since the OP claims he doesn't know. I brute forced it with a program.
There are
First of all, there are ...
- 1,935
34
votes
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32
votes
Accepted
32
votes
Accepted
16 pawns on a chess board with no three collinear: how do I go about solving this?
The Algoritm is :
Then
Here is the complete solution from Achim Flammenkamp Ph.D.
There are totally 57 solutions
- 17.8k
30
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Desegregate the Knights
Give these names to all the squares:
163
4 8
725
Each number can only be accessed by way of the numbers before and after it (where 8 wraps around to 1). That ...
- 145k
30
votes
Accepted
Could you solve a chessboard math puzzle at gunpoint?
Suppose that we have a chessboard with the desired properties.
Find the greatest number in each row. Out of these numbers, let the smallest be $m_i$ in row $i$.
Find the smallest number in each row....
- 33.6k
29
votes
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Chessboard Rook Problem
There are
Proof:
Now
I bet the ratio of good to bad is
I wrote a little Python program (possibly buggy, so apply some skepticism, but I've tested the bit most likely to have bugs and it seems OK) ...
- 117k
29
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Chess solitaire: The King's longest walk
First solution - 50 moves
Second solution - 59 moves
Current solution - 66 moves (beaten by Retudin - 70 moves and Rewan Demontay - 139 moves)
Moves:
- 18k
27
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Switch The Knights
I found a solution that uses 16 moves.
After exhaustively checking that there is no solution in 14 moves, I conclude that 16 moves is optimal, because after any odd number of moves the number of ...
- 13.5k
27
votes
Accepted
Two Knights, two Bishops, two Rooks and two Kings on a 4x4 chessboard
I hope I didn't make any mistakes:
Edit : Replace queens by king
- 524
27
votes
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26
votes
Accepted
25
votes
Accepted
The Popular Letter Chessboard
The rules of the question state that:
On your final grid, a letter (actually several is also mathematically possible) will be more frequent than all the other letters. Your aim is that this letter ...
- 134k
25
votes
The Knight's Romp
I have a computer program for solving packing problems, and found a way to use it to solve this problem. One of the solutions it found is below:
Note that this is very close to the attempted solution ...
- 50.8k
24
votes
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23
votes
Two Knights, two Bishops, two Rooks and two Kings on a 4x4 chessboard
Here is mine with passive kings, some minutes late :
- 3,070
22
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Switch The Knights
You need at least 16 Moves.
Let's make the task visually more simple. The initial board is:
a4 b4 c4
a3 b3 c3
a2 b2 c2
a1 b1 c1
We cut it into 12 cells ...
- 16.1k
22
votes
Accepted
Paint 21 Squares of a 7×7 Board Without Forming a Rectangle
Here's the solution:
There's a very neat method for finding this, inspired by the no-computers way of solving another related puzzle. Namely,
More specifically, given the constraints of this problem:...
- 116k
22
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Four fanatics and one checkerboard
I'm not sure why you'd need ANY sort of dissection for this.
- 2,757
22
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A Rook's Territory in the Chessboard
I started with this:
Pushed things this way and that, ended up with this:
Similarly, on 9x9:
And on 10x10:
It took me a while to get there, but that one suggests an emerging pattern.
And here is ...
- 13.4k
21
votes
20
votes
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Checkmate N Kings with M Knights
50 Kings,14 Knights:
This is optimal but not unique, see bottom of this answer.
Reasoning:
I think the problem is equivalent to covering every square on the board with as few knights as possible and ...
- 19.1k
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