54
votes
How can 3 queens control the white squares?
I think this arrangement works for the bonus question:
48
votes
Accepted
33
votes
Accepted
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.
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:
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 ...
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.
26
votes
Accepted
25
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 ...
24
votes
Accepted
24
votes
Accepted
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 ...
24
votes
24
votes
22
votes
Accepted
What is the least number of colours Peter could use to color the 3x3 square?
The minimum is
because
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:
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
...
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"
20
votes
Accepted
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,
19
votes
Accepted
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 ...
18
votes
Accepted
18
votes
Accepted
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 ...
17
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:
...
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 ...
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:
15
votes
Accepted
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 ...
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 ...
15
votes
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.
Only top scored, non community-wiki answers of a minimum length are eligible
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