66
votes
Accepted
56
votes
Accepted
52
votes
How can 3 queens control the white squares?
I think this arrangement works for the bonus question:
- 1,703
47
votes
Accepted
39
votes
Accepted
38
votes
Accepted
37
votes
Accepted
Black wants to go first!
Proof:
Initially, there are an even number of knights on white squares (namely, there are two of them, at b1 and g8).
Every time a knight moves, the number of knights on white squares either ...
- 31.7k
36
votes
34
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 ...
- 21.7k
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
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
- 17.7k
31
votes
Accepted
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 ...
- 143k
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....
- 33.4k
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) ...
- 115k
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:
- 17.9k
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 ...
- 13.4k
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
Accepted
26
votes
The coolest checkerboard magic trick
This indeed is an old puzzle. One possible source (but certainly not the first one) is:
Andy Liu: Two Applications of a Hamming Code
The College Mathematics Journal 40, (Jan 2009), pp. 2-5
The ...
- 45k
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 ...
- 117k
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 ...
- 47.3k
23
votes
Accepted
23
votes
Accepted
Tiling a Chessboard with tetrominos
It is not possible. The area of a $10 \times 10$ checkerboard is $100$, so it takes $25$ T pieces to have the same area. The checkerboard has the same number of red and black squares, but each piece ...
- 7,146
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
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 ...
- 16k
22
votes
Four fanatics and one checkerboard
I'm not sure why you'd need ANY sort of dissection for this.
- 2,757
21
votes
Black wants to go first!
While (as other answers proved it) it is impossible to solve this just by using knights, the problem can still be solved.
Matthew says "As I want to play white, my first move isn't really a secret. ...
- 1,704
21
votes
Accepted
Checkerboard Infection
This is a pretty common puzzle.
Warm up Answer:
Advanced Answer Explanation:
- 1,519
Only top scored, non community-wiki answers of a minimum length are eligible
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