66
votes
Accepted
56
votes
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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
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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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34
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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
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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
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30
votes
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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 ...
- 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
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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) ...
- 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
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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 ...
- 13.4k
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
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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
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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
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23
votes
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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
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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 ...
- 16k
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
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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:
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