Questions tagged [construction]
A puzzle that requires an example to be built that fits certain criteria.
88
questions
7
votes
2answers
212 views
Gentrification in Chessshire
You can skip the back story and directly jump to the question.
Capitalism has arrived in suburban Chesster the community most famed for The Game, and with a vengeance. Rents have trebled in less than ...
0
votes
1answer
79 views
Self-indulgent numbers
Let's call a positive integer N self-indulgent of degree K>2 if for every positive integer k<K the following is true:
More than half of the first k multiples N,2N,...,kN of N contain with ...
3
votes
1answer
188 views
Infinite beauty
This is a follow-up to Puzzle about 6 infinite cylinders in space
Question:
Given six identical infinite (no caps) cylinders is there a beautiful arrangement in space such that each touches each ...
10
votes
2answers
644 views
Never kill your king … without first seeking proper legal advice!
This is a follow-up to (Almost) all hands on check by @loopy walt.
The task (mate in one with as many essential pieces as possible) stays the same, but you are to go about it more cunningly.
Recap of ...
8
votes
3answers
959 views
(Almost) all hands on check
Historical note (skip if you like):
In this interesting puzzle @TSLF asks for the "maximum number of black and white pieces that are involved in a checkmate position".
Originally, they left ...
1
vote
2answers
200 views
Four pacifist queens
Earlier, I introduced the beautiful game of Swiss chess.
These are animated gifs. You may have to click on them to make them move.
Unlike the peace-loving Swiss, we are interested in "domination&...
5
votes
1answer
255 views
Four queens on public transport
The enlightened but, sadly, fictional country of Switzerland has it all: A strong democracy that resists centralism, a reliable public transport network and its own version of chess.
Swiss chess ...
3
votes
1answer
169 views
Universal bisectors
A bisector is something that cuts some other thing into two equal pieces. More concretely, assume we are given a reasonably well-behaved (for example, compact) 3D object and we are looking for planes ...
5
votes
1answer
172 views
Anti-Chess Squares
Playing regular rules for both white and black try to eliminate all the square formations by black and/or white. From the above starting setup all rooks form a square. Also white's queen rook pawn, ...
0
votes
1answer
36 views
A rectangle with non-integer side lengths [duplicate]
Is it possible to build a gapless rectangle with non-integer side lengths using rectangles each with two integer side length and two non-integer side length?
The rectangles are not required to be the ...
2
votes
1answer
183 views
Piercing Bullets
Under 30-secs. bullet time control the above position results after n moves. What is the fewest number of moves possible?
30
votes
5answers
5k views
How can 3 queens control the white squares?
It is well known that there is no way of arranging 4 queens on a checker board in such a way that every square is occupied or threatened.
Now consider a slight variation where we only need to cover ...
5
votes
1answer
286 views
Triangles, rectangles, nonagons
Which is the nonagon with the least area and which fulfills the following conditions.
The nonagon has to be made from 7 triangles and 3 rectangles, all having side-lengths that are integer numbers.
...
4
votes
3answers
174 views
Experts at failure
Construction challenge:
Find a position with the longest sequence of unique losing moves, i.e. white to move has one and only one move that will lead to a lost (for white) position. White makes this ...
8
votes
1answer
516 views
Doubly Pure Checkmate
A pure checkmate is a checkmate where for each square the king might go to, there’s exactly one reason it can’t. The famous Légal mate is one example, so is a KR vs K checkmate.
What’s the minimum ...
-1
votes
1answer
107 views
10X10 Sudoku with a specific requirement
Let's have a 10x10 grid. We want to create a Sudoku in which, in each row, the pairs (a+b), (c+d), (e+f), (g+h), (i+j) add to one of the following numbers: 7, 9, 11, 13, or 15. Can you construct a ...
7
votes
2answers
278 views
Black board attack
How should Black move as to attack all the squares that have no piece on them with only ten legal moves for black? Any unoccupied squares must be attacked. Start from the position above as shown.
10
votes
1answer
211 views
Chess Construction Challenge #5: Can't pass-ant up the chance!
For the end of the year, here is a random challenge to boggle your brains!
Given that:
White has their king, a queen, two rooks, a knight, and seven pawns
Black has their king and seven pawns
...
11
votes
4answers
927 views
Consecutive captures on the same square
What is the most number of consecutive captures that you can have on the same square in a standard game of chess? Assume that black and white alternate in taking turns. Good luck!
11
votes
2answers
602 views
Advantage, Black!
In chess, the white player makes the first move. It is generally understood that this gives white a minor advantage, with a win rate of 52-56%.
In this initial position, white actually has checkmate ...
5
votes
4answers
416 views
Most Captures Chess
In Most Captures Chess puzzle, you will need to provide a legal game where it is Blacks to play and where they have the most different ways to capture a White piece.
For instance, the next game allows ...
4
votes
1answer
141 views
Day-in-the-sun chess
Inspired by this puzzle: Doubled Knights redux
Let's make the following change to the rules of chess. Every piece can once per game (on its day in the sun) make a double move.
Clarifications:
Things ...
5
votes
3answers
263 views
A tribute to “Most ways to uncheck the king”
Today, we had the great privilege to see @Paul Panzer's answer being ticked at @thesilican's absorbing puzzle.
I here propose a variant of his puzzle where it's not mandatory to use a legal chess game....
19
votes
4answers
2k views
Most ways to uncheck the king
Here's my attempt at a chess puzzle
Your task is to construct a legal chess position where:
It is black's turn to move
Black is in check
Black has the greatest number of different legal moves ...
12
votes
2answers
628 views
Chain Puzzle: Tabletop Games #7 - Maze
This is the seventh Chain Puzzle in the Tabletop Games series, in which all puzzles are themed around board games, card games, tile games, and the like. The answer to this puzzle is a thematic word or ...
19
votes
1answer
1k views
Ernie and the Lock-down Puzzle
During lock-down I was feeling a bit lost for something to do, so one one day I sent Ernie a text reading "Bored".
He responded with a text-less message and an attached image (see below).
I ...
5
votes
2answers
219 views
Escape the Plane
One Sunday morning, you awake to find yourself completely alone on an infinite, flat plane. You don't remember much about the night before, other than that you may have pissed off a wizard. Next to ...
9
votes
3answers
512 views
The Existence of Total False Sudoku
Is it possible to construct a valid 9x9 puzzle of Total False Sudoku?
Total False Sudoku is a regular Sudoku puzzle where all given clue numbers are wrong. A valid puzzle is a puzzle that has only a ...
3
votes
2answers
471 views
A Puzzle about “Codeforces Subsequences”
I'm quite intrigued by an "easy" problem in recent Codeforces contest: Codeforces Subsequences.
In this problem, you have to create a string $T$ as shortest as possible such that $S = $ &...
23
votes
2answers
4k views
What if I told you that guessing in Sudoku is very bad and might give you a bad karma?
Yesterday, I tried to solve a regular Sudoku puzzle. Of course, the Sudoku puzzle had a unique solution. But, I was feeling a little lazy, so, rather than solve the puzzle properly, I made guesses! At ...
4
votes
2answers
200 views
Chess Construction Challenge #4-Excelsior!
It’s been awhile since the last one, so cheers for round four!
Given that:
It’s White to selfmate themselves in exactly 5 moves, i.e. after White’s fifth move, Black’s only legal move(s) will ...
10
votes
2answers
200 views
Mark Two Points Which Have a Distance of $\sqrt{3.6}$
Here is a grid graph with $7$ horizontal and $7$ vertical lines which are $1$ unit apart. It is trivial to mark two points which have a distance of $\sqrt{36}$.
Drawing at most two extra lines as ...
19
votes
1answer
1k views
Your Task Is to Create the World's Hardest Irregular Sudoku!
Ahem, let's formalize your task...
A Sudoku is a puzzle consisting of a grid to be filled with symbols, such that each constraining unit contains each symbol exactly once. The regular Sudoku is a $9 \...
8
votes
1answer
320 views
Constructing an island according to rules in Smullyan's “What is the Name of this Book”
I've recently finished dropping my jaw at Raymond Smullyan's "What is the Name of this Book," and the section on Gödel's incompleteness theorem, involving islands of knights (truthers) and knaves (...
5
votes
1answer
175 views
Symetrical, locked Othello game
This is an unusual ask, but bear with me...
One night back in the 1970's. I was playing Othello with a friend when I realised that, not only were there no more moves with four empty spaces remaining ...
9
votes
1answer
535 views
Connect the wires without setting off the bomb
You just saw a planted time bomb! Just 5 minutes are remaining until it explodes and as you are in currently in a rural area (no bomb disposal squad) and you know how bombs usually work it is up to ...
6
votes
1answer
549 views
Chess Construction Challenge #2-Check!
It’s time for round two!
Given that:
Black has 6 pawns and a king
White has three pieces of any kind you to deduce the identity of and a king
Construct:
A legal position in which both sides help ...
4
votes
2answers
231 views
Chess Construction Challenge #1-Read First Please!
I'm starting a new series in which I set a very specific goal with a unique (to be more specifically defined here in a bit) answer in which the solver must construct a chess position, sometimes a game,...
7
votes
2answers
291 views
A pyramid from a square
Given a square piece of paper. Cut it into 4 pieces that could be used to create a right angle pyramid - the 4 pieces are the faces of the pyramid.
5
votes
1answer
416 views
Something Large From Something Small
I have created a miniature chess puzzle that takes advantage of a piece of chess semantics that has some debate to it.
This is the puzzle:
Construct a legal (meaning that two opposite colored Kings ...
6
votes
1answer
382 views
Polygon Construction for Specified Number of Interior and Boundary Lattice Points
Construct a simple polygon on a grid of equal-distanced points such that:
all the polygon's vertices are grid points,
there are exactly $i~(\geq 0)$ lattice points in the interior, and
...
14
votes
4answers
592 views
Racetrack designers, assemble!
Note: Turns out the intended answer to this doesn't work after all (see comments to Sconibulus's answer). The rules have been changed slightly after the fact to ensure there can be valid answers (see ...
7
votes
2answers
1k views
Unknown 5-pieces cube puzzle - help recognize
I have strange 5-pieces cube puzzle which I can't solve for a long time. I don't know name of the puzzle and can't google it. I'm not sure that there are all pieces. Can you help to recognize it?
...
6
votes
2answers
231 views
The Fastest Way-A Challenge
This is my first “find the fastest way to this position” chess puzzle” here on PSE. However, this is not for just some random position. Let me explain.
Tim Krabbe has said on his site (Journal Entry ...
5
votes
2answers
383 views
Build Me A Pawn Wall!
I have a very unique chess construction task for you all today: Build me a pawn wall!
I challenge you to construct a game that ends with both sides having 6 pawns on a file. This means that 6 white ...
5
votes
2answers
185 views
How to fill $4320$ multiplicative semi-magic square?
How can we fill $4*4$ Matrix with distinct positive integers such that product of the entries in each row & column is equal to $4320$ ?
My Strategy:
$$4320=2^5 \times 3^3 \times 5$$
First I ...
10
votes
2answers
591 views
Missing checkmates in one
Have you ever missed a one-move checkmate and immediately realized it after making your move? If you have, you just might have what it takes to crack this problem. Let's take an example:
g4 e5
...
13
votes
2answers
383 views
Geometry From Hell
You’re locked in a room with nothing but a pencil, a math compass, and paper. You do not have a straightedge. Your captors have informed you that you cannot leave until you construct (the endpoints of)...
6
votes
1answer
719 views
Is there a configuration of the 8-puzzle where locking a tile makes it harder?
I am trying to find a starting configuration of the standard 3×3 8-tile sliding block puzzle that is harder to solve (i.e. takes more moves, but is still solvable) when one of the blocks is locked in ...
21
votes
2answers
3k views
The Longest Chess Game
In honour of Stockfish and Leela Chess Zero just finishing the longest game in TCEC history at the Superfinal of the Top Chess Engines Championship Season 14, here's a simple problem related to chess ...
