65 votes
Accepted

Cover 63 squares of a chess board

These should do it: Just to show another example:
  • 5,140
56 votes
Accepted

Crippled King Crossing a Canyon

Explanation:
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50 votes

How can 3 queens control the white squares?

I think this arrangement works for the bonus question:
  • 1,683
46 votes
Accepted

How can 3 queens control the white squares?

I think this will do it
  • 126k
38 votes
Accepted

A lonely pawn on the chessboard

Strategy: How this works:
38 votes
Accepted

Rooks on a 15x15 chessboard

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37 votes
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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 ...
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36 votes

Chessboard Rook Problem

There are more ones. Proof:
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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 ...
  • 21.5k
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

A chess board with numbers

The smallest sum that can be achieved is Because Reasoning
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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
31 votes
Accepted

Mutilated chessboard

I believe this works as a short proof.
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....
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29 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 ...
  • 141k
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:
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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 ...
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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
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27 votes
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Playing with one Queen on a chessboard

We can work backwards to figure this out: Conclusion:
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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 ...
  • 44.9k
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 ...
  • 109k
24 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 ...
23 votes
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Two rooks for Bobby Fischer

Answer:
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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 ...
23 votes

Two Knights, two Bishops, two Rooks and two Kings on a 4x4 chessboard

Here is mine with passive kings, some minutes late :
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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 ...
  • 15.9k
22 votes

Four fanatics and one checkerboard

I'm not sure why you'd need ANY sort of dissection for this.
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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. ...
  • 1,684
21 votes
Accepted

Checkerboard Infection

This is a pretty common puzzle. Warm up Answer: Advanced Answer Explanation:
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