54 votes

How can 3 queens control the white squares?

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

How can 3 queens control the white squares?

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

How did four chessmen disappear?

This seems to work: And the position looks like this: Apart from the symmetrical solution, this might very well be unique:
Bass's user avatar
  • 77.4k
29 votes
Accepted

Ernie and the Lock-down Puzzle

Ernie's jigsaw puzzle isn't as straightforward as it seems, as it's actually: One way of assembling the pieces legally is: How will you know when you have succeeded? PS Ernie definitely has a sense ...
Stiv's user avatar
  • 141k
28 votes

A pentagon that can measure the first 7 integer distances

A possibly more elegant solution for 1..7 if we don't insist on a convex pentagon.
Florian F's user avatar
  • 29.8k
26 votes
Accepted

What if I told you that guessing in Sudoku is very bad and might give you a bad karma?

You're
Glorfindel's user avatar
24 votes
Accepted

Most ways to uncheck the king

Eeny meeny myny moo (or however you want to spell that)
Paul Panzer's user avatar
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24 votes
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Consecutive captures on the same square

Since we are talking about a standard game of chess (although with both players co-operating), we know that there are four pieces that cannot possibly make a capture in the series: the two bishops on ...
Bass's user avatar
  • 77.4k
24 votes

Efficient Mowing at PSE

Proof of optimality for the solutions given
Florian F's user avatar
  • 29.8k
24 votes

Mishustin's circle problem

daw's user avatar
  • 3,178
24 votes
Accepted

Mishustin's circle problem

Here's my go (click to embiggen) Steps: Connect A to P and pick an arbitrary point Q between them, near-ish to P. Then, draw lines as shown, constructing the points in alphabetical order, which ...
Bass's user avatar
  • 77.4k
21 votes
Accepted

Your Task Is to Create the World's Hardest Irregular Sudoku!

The 'hardest' possible Irregular Sudoku has and it looks like this:
Deusovi's user avatar
  • 146k
21 votes

Chess Construction Challenge #6: The One Move Royale

Vepir has helped twice in this answer, first in spotting a mistake and then with an improvement in the number of moves. Please got upvote their answer too if you like this one. Here is a position with ...
hexomino's user avatar
  • 136k
19 votes

What if I told you that guessing in Sudoku is very bad and might give you a bad karma?

Glorfindel's answer is sufficient for the main question. To answer the bonus question: Here is an example: To construct this example, As for a starting position,
Brilliand's user avatar
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19 votes
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A pentagon that can measure the first 7 integer distances

The answer is This can be proven by
noedne's user avatar
  • 15.4k
18 votes
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The Longest Chess Game

My answer is Explanation:
Jaap Scherphuis's user avatar
18 votes

A pentagon that can measure the first 7 integer distances

Dennis_E's user avatar
  • 1,209
16 votes
Accepted

The Game of Golden Squares

I've achieved tiles, and can prove that this is the optimal solution. Reasoning: Golly 4.0+ pastable RLE of this solution: ...
Magma's user avatar
  • 5,259
15 votes

Create a 1 meter measure

I can do it in just: Initial configuration: First: We have: Now: We get the mark: Finally: You get: And the required distance is: Why this works:
boboquack's user avatar
  • 22k
14 votes
Accepted

No moves at all, not even to put yourself in check

Here are my first idea (both sides are essentially the same answer, so the hint fits too): Both positions seem to be independently reachable by a legal game. It might be possible to find a legal game ...
Bass's user avatar
  • 77.4k
14 votes
Accepted

Is there a configuration of the 8-puzzle where locking a tile makes it harder?

As far as I know, the only way to figure this out is by letting a computer run through all the possibilities. It is a small puzzle, so this does not take long. First I will assume that you want the ...
Jaap Scherphuis's user avatar
14 votes

Chess Construction Challenge #6: The One Move Royale

Score: Position: Moves: Fun fact,
Vepir's user avatar
  • 2,936
14 votes
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What's the most distant chess position?

This question was asked on Chess Stack Exchange a couple of years ago: Which chess position requires the most moves to reach? Just like @loopywalt here in the comments, I remembered Tim Krabbé's diary ...
Glorfindel's user avatar
13 votes
Accepted

Geometry From Hell

Suppose you can set your pair of compasses to length 1. Then Then we know that the length of the line that would join those two points is The simplest construction would use:
Dr Xorile's user avatar
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13 votes
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Mark Two Points Which Have a Distance of $\sqrt{3.6}$

Of course we need to use Pythagoras. This leads to the following solution: Here is another more compact solution.
Jaap Scherphuis's user avatar
13 votes

Advantage, Black!

This should do it: White is in zugzwang, so black has
Bass's user avatar
  • 77.4k
13 votes
Accepted

A Tetris puzzle made with love

I managed to copy the initial position wrong, and spent several hours without finding a proper solution to the warm-up question. Ouch. Well, at least I learned a lot about this puzzle type, and you ...
Bass's user avatar
  • 77.4k
13 votes
Accepted

Efficient Mowing at PSE

Others of the same length exist, such as this, this and SQLNoob's, and several more. Proof of optimality (see FlorianF's for a more concrete proof: TL;DR:
Beastly Gerbil's user avatar
13 votes

What's the most distant chess position?

I will open the bidding at I won’t offer a series of moves, but describe the position as To see that this would take at least as many moves as claimed, note that In fact
Daniel S's user avatar
  • 6,748
12 votes
Accepted

Chess Construction Challenge #2-Check!

My position has a fourteenth check too, but that's probably ok. :-) These are the moves: And here's the whole solution uploaded to Lichess. EDIT: Looks like 15 is also doable: The final check ...
Bass's user avatar
  • 77.4k

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