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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
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How can 3 queens control the white squares?

I think this will do it
hexomino's user avatar
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33 votes
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Place some or all of the White Chess pieces on a chessboard in such a way that none of them can legally move

Here's a solution I created just now that uses every piece.
TakingNotes's user avatar
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29 votes
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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
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29 votes
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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
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29 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
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26 votes
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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
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25 votes
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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
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24 votes
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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
  • 80k
24 votes

Efficient Mowing at PSE

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

Mishustin's circle problem

daw's user avatar
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22 votes
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What is the least number of colours Peter could use to color the 3x3 square?

The minimum is because
xnor's user avatar
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21 votes
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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
  • 151k
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
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21 votes

Can you arrange 25 whole numbers (not necessarily all different) so that the sum of any three successive terms is even but the sum of all 25 is odd?

There are only two possible solutions (disregarding meaningless number swaps). Explanation What I mean by "meaningless number swaps"
Hilmar's user avatar
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20 votes
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Make exactly 101 squares using as few lines as possible

I can do it in lines.
Lezzup's user avatar
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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
  • 904
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
  • 19.1k
19 votes

Make exactly 101 squares using as few lines as possible

I'm hoping it's within the rules, but if so: It works for any number of squares! I'm unfortunately not familiar with any tools to generate an image for this, but the approach is: For a better ...
Daniël van den Berg's user avatar
18 votes
Accepted

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
  • 1,219
18 votes
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Are these colored sets closed under multiplication?

Question 1: Is it necessarily true that at least one of the sets is closed under multiplication? Question 2: Is it necessarily true that both sets are closed under multiplication? Question 3: Is it ...
msh210's user avatar
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17 votes
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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
  • 5,384
16 votes

What is the least number of colours Peter could use to color the 3x3 square?

Basically a beginner here. Start with a diagonal. All three cells must have unique colours: Then, the two unshaded corners must be given unique colours because both of them have a diagonal with the ...
matt_rule's user avatar
  • 654
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
  • 22.1k
15 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
  • 28.2k
15 votes

Make exactly 101 squares using as few lines as possible

I can match Lezzup's record of using only infinite straight lines: I'm pretty sure this is the minimum attainable, since For the record, Dudeney's version can be also solved with the same number of ...
Bubbler's user avatar
  • 17.1k
15 votes

Can you color the 8x8 grid red and blue?

Here is one way you can do it: Alternatively:
PDT's user avatar
  • 21.8k
15 votes

Can you color the 8x8 grid red and blue?

Some more fun solutions: Both satisfy the following self-imposed restrictions: Each row and each column contains exactly four blue and four red squares. The grid is symmetric in some way.
Bubbler's user avatar
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