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:
48
votes
Accepted
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 ...
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 ...
34
votes
Accepted
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
30
votes
Accepted
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 ...
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....
29
votes
Accepted
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) ...
29
votes
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:
27
votes
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 ...
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
27
votes
Accepted
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 ...
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 ...
24
votes
Accepted
23
votes
Two Knights, two Bishops, two Rooks and two Kings on a 4x4 chessboard
Here is mine with passive kings, some minutes late :
22
votes
Accepted
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 ...
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:...
22
votes
Four fanatics and one checkerboard
I'm not sure why you'd need ANY sort of dissection for this.
22
votes
Accepted
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 ...
21
votes
20
votes
Accepted
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 ...
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