Questions tagged [construction]
A puzzle that requires an example to be built that fits certain criteria.
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Logical Deduction Persistence Test
In the grid below, create a path that starts at cell 1 and ends at cell 49, moving horizontally and vertically only.
The path must touch each of the 49 cells exactly once and contain a:
A. Maximum of ...
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A pentagon that can measure the first 7 integer distances
A pentagon can be used to measure 10 distances - one distance between each pair of its 5 vertices. Can you find a pentagon that can measure every integer distance from 1 to 7, inclusive?
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Efficient Mowing at PSE
Your task:
Find the most efficient mowing path around the dark green bushes that mows (passes over) all of the grass (light green).
For those who cannot view the image above, there are 9 rows of 16, ...
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Symmetrical Chess Position With No Legal Moves
Your task is to set up a symmetrical (both vertically and horizontally) position on the first 7 ranks of a chess board that meet all of the criteria below.
For this puzzle, there is no eighth rank. It ...
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The Game of Golden Squares
On a magic chessboard of infinite size, the squares are either wooden or golden. If 4 or more of its 8 neighbors (a king's move away) are golden, a wooden square becomes golden the next day. Golden ...
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4x4 word 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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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(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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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