Questions tagged [construction]

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

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4x4 words grid optimization

Given that each letter in the English alphabet has a position: $$a = 1, b = 2, ..., z = 26$$ Can you place 16 different letters such that: Each row, column and diagonal forms a 4 letter valid English ...
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21 votes
2 answers
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A Tetris puzzle made with love

I love designing perfect clear puzzles for my dear friend who loves Tetris. Here's a lovely puzzle I crafted today. Original Puzzle (Warm-Up) Starting with this field, place this exact sequence of ...
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10 votes
2 answers
505 views

Permutations of first 10 natural numbers such that all the prefix sums are distinct

I posted this question on Math SE as well. Did not receive any help. This is a question that I was asked in a Quant Interview. I would like you all to have a crack at this. I could not find a problem ...
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3 votes
2 answers
233 views

Quickest mate with Queens exchange

If both players cooperate, what is the quickest mate in chess that includes a Queens exchange, in a legal game?
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7 votes
1 answer
224 views

Smallest number of moves to reach a "reverse checkers" position

A "reverse checkers" position is a position where every piece for one player is on one colour and every piece for the other player is on the other colour. Consider this position, for example:...
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10 votes
0 answers
135 views

Rigid regular nonagon from 21 Meccano strips

You are given 21 Meccano strips, where the distance between adjacent holes is 1 unit: 9 strips of length 10 (hence having 11 holes) 6 strips of length 18 (19 holes) 6 strips of length 19 (20 holes) ...
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2 votes
1 answer
95 views

Make a topological torus-with-a-hole out of congruent squares that may share an edge or a vertex with other squares

Suppose we arrange, in 3-dimensional space, 8 identical solid cubes in space so they form a square-shaped ring (using a 3x3 arrangement of squares except for the one in the middle). Its surface will ...
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10 votes
2 answers
467 views

Clash of the Robinsons

"Ridiculous!" you think "What can be the odds? Either I'm hallucinating or the amateur writing this story plunged to new depths of incompetence." Both being equally likely you don'...
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4 votes
2 answers
434 views

Longest chain of checks and captures

On a standard size chessboard, with white to move, make a configuration of chess pieces and moves, so that with every move by white the black king repeatedly becomes checked. With every move black ...
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8 votes
0 answers
233 views

Doubling the cube with rational Meccano strips

In three monographs published in 2006, 2008 and 2014 Gerard 't Hooft considered "Meccano mathematics": how to construct specified distances and regular polygons by a rigid system of ideal ...
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3 votes
3 answers
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Chess Construction Challenge #9: Two Eggs & A Flood

I have an odd idea for this challenge. It involves a very specific proof game construction. So pay attention! Given that: White and Black cannot move more than one pawn each throughout the entire ...
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3 votes
2 answers
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Chess Construction Challenge #D: 8 moves

Since I "burnt" the complete question elsewhere, let's start with "D" (I counted up in hex) and 8 moves. The position in the answer there can be improved by far! OK, to ...
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3 votes
1 answer
143 views

Chess Construction Challenge #8: Three Times The Charm

On a chessboard, a piece has a set number of legal moves. It can range from 0 to 27. However, this amount can also restricted. My previous questions have covered n=1 and n=2, it is time for n=3! Given ...
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6 votes
1 answer
590 views

Flat share share

This is a sequel to Gentrification in Chessshire. Due to the febrile state of the Chesster housing market you and your flat mates are forced to rent out half your place to another group of sharers. ...
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7 votes
3 answers
525 views

Chess Construction Challenge #7: Double The Fun

Many thanks goes to @Retudin in a comment on my last question for this idea. In a chess position, pieces can be restricted as to how many moves they can legally make in theory. Since my previous ...
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9 votes
5 answers
1k views

Chess Construction Challenge #6: The One Move Royale

In chess, it is possible for a piece to have only one legal move. For example, in this position, the Black king can move only to h2. Given that: All 32 pieces are available for use. Construct: A ...
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9 votes
2 answers
358 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 ...
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0 votes
1 answer
96 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 ...
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4 votes
1 answer
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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 ...
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11 votes
2 answers
757 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 ...
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10 votes
3 answers
1k 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 ...
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1 vote
2 answers
224 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&...
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5 votes
1 answer
299 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 ...
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3 votes
1 answer
181 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 ...
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5 votes
1 answer
226 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, ...
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0 votes
1 answer
58 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 ...
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2 votes
1 answer
210 views

Piercing Bullets

Under 30-secs. bullet time control the above position results after n moves. What is the fewest number of moves possible?
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30 votes
5 answers
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 ...
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6 votes
1 answer
308 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. ...
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4 votes
3 answers
191 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 ...
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8 votes
1 answer
538 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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-1 votes
1 answer
127 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 ...
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8 votes
2 answers
300 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.
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3 votes
3 answers
195 views

Footmen and Friends #4: Double Iced

It's time for Episode 4 after a long time off air! This time, it's another unusual dazzle. It's a short, but succulent, sweet New Year's treat. In the starting position, with no pieces other than the ...
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10 votes
1 answer
253 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 ...
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11 votes
4 answers
963 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!
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10 votes
2 answers
618 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 ...
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5 votes
4 answers
456 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 ...
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4 votes
1 answer
186 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 ...
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5 votes
3 answers
286 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....
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18 votes
4 answers
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 ...
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  • 2,374
11 votes
2 answers
699 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 ...
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  • 4,767
19 votes
1 answer
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 ...
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6 votes
2 answers
237 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 ...
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9 votes
3 answers
545 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 ...
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3 votes
2 answers
522 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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23 votes
2 answers
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 ...
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4 votes
2 answers
252 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 ...
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10 votes
2 answers
207 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 ...
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19 votes
1 answer
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 \...
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