67 votes
Accepted

Cover 63 squares of a chess board

These should do it: Just to show another example:
hdsdv's user avatar
  • 5,190
57 votes
Accepted

Crippled King Crossing a Canyon

Explanation:
f'''s user avatar
  • 33.7k
54 votes

How can 3 queens control the white squares?

I think this arrangement works for the bonus question:
Zoir's user avatar
  • 1,723
48 votes
Accepted

How can 3 queens control the white squares?

I think this will do it
hexomino's user avatar
  • 136k
39 votes
Accepted

Rooks on a 15x15 chessboard

Slepz's user avatar
  • 1,438
36 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 ...
humn's user avatar
  • 21.9k
36 votes

Chessboard Rook Problem

There are more ones. Proof:
Nopalaa's user avatar
  • 849
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 ...
Reti43's user avatar
  • 1,935
34 votes
Accepted

A chess board with numbers

The smallest sum that can be achieved is Because Reasoning
hexomino's user avatar
  • 136k
33 votes
Accepted

Mutilated chessboard

I believe this works as a short proof.
Tyler Seacrest's user avatar
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
Jamal Senjaya's user avatar
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....
f'''s user avatar
  • 33.7k
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) ...
Gareth McCaughan's user avatar
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:
Sleafar's user avatar
  • 18.1k
28 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
Skyvask's user avatar
  • 534
27 votes
Accepted

Playing with one Queen on a chessboard

We can work backwards to figure this out: Conclusion:
Deusovi's user avatar
  • 146k
26 votes
Accepted

Chess with jumping

The result is a The idea is to Here's the line:
xnor's user avatar
  • 26.8k
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 ...
Stiv's user avatar
  • 142k
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 ...
Jaap Scherphuis's user avatar
24 votes
Accepted

Two-Move Chess Game

fblundun's user avatar
  • 1,536
23 votes

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

Here is mine with passive kings, some minutes late :
Saeïdryl's user avatar
  • 3,040
23 votes

Four fanatics and one checkerboard

I'm not sure why you'd need ANY sort of dissection for this.
Braegh's user avatar
  • 2,767
23 votes
Accepted

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 ...
Daniel Mathias's user avatar
22 votes
Accepted

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:...
Rand al'Thor's user avatar
22 votes

A Rook's Territory in the Chessboard

Here's an expandable solution for $n\ge 5$ (even or odd):
RobPratt's user avatar
  • 13.7k
20 votes
Accepted

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 ...
loopy walt's user avatar
  • 21.3k
20 votes
Accepted

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 ...
loopy walt's user avatar
  • 21.3k
19 votes

Discrete Peaceful Encampments: 9 queens on a chessboard

Nine queens of each color. Some variation is possible.
Daniel Mathias's user avatar
18 votes

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.
Daniel Duque's user avatar
18 votes
Accepted

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 ...
Jaap Scherphuis's user avatar

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