67
votes
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54
votes
How can 3 queens control the white squares?
I think this arrangement works for the bonus question:
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48
votes
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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 ...
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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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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
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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) ...
- 120k
29
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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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28
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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
- 534
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26
votes
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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 ...
- 146k
25
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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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25
votes
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24
votes
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How can the knight traverse a chessboard to make a path that sums to 100
The path is as follows:
I found this path after
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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 :
- 3,040
23
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Four fanatics and one checkerboard
I'm not sure why you'd need ANY sort of dissection for this.
- 2,767
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votes
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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 ...
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22
votes
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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:...
- 117k
22
votes
A Rook's Territory in the Chessboard
Here's an expandable solution for $n\ge 5$ (even or odd):
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20
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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 ...
- 21.3k
20
votes
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Coloring of a 5 x 5 chessboard
Borrowing ideas from both @Gareth and @xnor:
WLOG one column has at least 3 black squares. Discard the 2 other rows. If any of the 4 other columns has more than 1 black square we are done. We are left ...
- 21.3k
19
votes
Discrete Peaceful Encampments: 9 queens on a chessboard
Nine queens of each color. Some variation is possible.
- 15.4k
18
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How many queens can be on a chessboard without attacking each other?
Sorry for reviving a 5 years old question, but I can fit:
I hope to avoid downvotes by pointing out that this troll solution satisfies all the conditions of the original question.
- 549
18
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Beans under the chessboard
This puzzle could have almost have been given the
tag, though that may have given a big hint.
You can think of each rectangle you pick as a move,
Here is a proof for why this is the minimal number ...
- 53.9k
18
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17
votes
Two Knights, two Bishops, two Rooks and two Kings on a 4x4 chessboard
Here's a solution with the additional constraint that no piece may attack more than one piece:
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Only top scored, non community-wiki answers of a minimum length are eligible