65
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56
votes
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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
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41
votes
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How many chess pieces does it take to "cover" all spaces on a chessboard?
Yes. The minimum number of pieces required is 5.
5 queens can be places such that they cover every space on the board, as in the following example:
There are 12 such arrangements, along with ...
- 3,484
38
votes
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38
votes
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37
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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
34
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How many queens can be on a chessboard without attacking each other?
Because:
According to Wolfram-Alpha, there are
One possible solution is:
A list (and images!) of all
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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
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 ...
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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
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30
votes
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30
votes
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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....
- 33.2k
29
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 ...
- 136k
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) ...
- 111k
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
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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 ...
- 13.3k
27
votes
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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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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 ...
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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 ...
- 93.5k
24
votes
How many chess pieces does it take to "cover" all spaces on a chessboard?
This type of chess puzzle is known as a domination problem, and as @Xynariz points out, only five queens are needed for the 8x8 board. It's also interesting to note that five queens are also ...
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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 ...
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23
votes
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23
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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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Moving a pawn around on a chessboard
No.
Every move the pawn makes it switches from a white to a black square or vice versa. Therefore it must either touch an equal number of white and black squares with an even number of moves, or one ...
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