Questions tagged [construction]

A puzzle that requires an example to be built that fits certain criteria.

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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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 ...
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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 = $ &...
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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 ...