Questions tagged [construction]

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

Filter by
Sorted by
Tagged with
3
votes
2answers
414 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
155 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
197 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
961 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
272 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
149 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
520 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
542 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
216 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
287 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
415 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
373 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
584 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
909 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? ...
4
votes
1answer
161 views

The Fastest Way-A Special Positional 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
379 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
175 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 ...
9
votes
2answers
544 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
377 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
709 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 ...
19
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 ...
4
votes
1answer
220 views

The Housing Estate

A constructor wishes to build a housing estate in a square terrain with 64 (8 x 8) smaller plots of land, at most one house to a plot. Local urban rules allow building a house in a plot only if at ...
3
votes
1answer
136 views

A construction toy for children [closed]

Alice has an idea for a construction toy made from plastic. Each building block is in the shape of an uppercase letter of the alphabet. No other characters are to be used. Children will ...
14
votes
3answers
1k views

No moves at all, not even to put yourself in check

Here, white is stalemated. The king is not in check, but white has no legal moves. Not because any move white makes would put the king in check -- which is how stalemates normally happen -- but ...
8
votes
3answers
401 views

Fabi and Mag played chess again

Fabi and Mag love chess, and I love to watch them playing together. I am not such a strong player myself, but I am an excellent spectator! The three of us were having a nice evening around a chess ...
26
votes
3answers
3k views

How did four chessmen disappear?

I was visiting two friends yesterday and found them sitting at a chess table. After a glance at the board, I thought I had interrupted them when they were installing the starting position and I said: ...
7
votes
2answers
224 views

Retrograde Go Problem (Some Assembly Required)

An entry into the Fortnightly Topic Challenge #40. In case you aren't familiar with the rules of go, the information in the basic rules section of the Wikipedia page should be enough to solve this ...
-1
votes
2answers
189 views

Chess amazement

Can you make a position where neither team can move anywhere? You can place the pieces anywhere, since it doesn't have to be in an actual game. This would be really easy, but I am so sorry to say ...
-2
votes
2answers
119 views

How many are they, how much do you owe them? [closed]

Let's suppose you want to build a house. To do this, you're going to need people to help build the house. Specifically, you're going to need contractors, engineers, and construction workers. After ...
5
votes
1answer
152 views

All the King's Horses and All the King's Men

What is the largest N by N square chessboard where it's possible to construct a position such that 2 knights and N pawns either occupy or threaten every square?
12
votes
3answers
348 views

A Floating Row - Tetris Puzzle

It is possible to produce the following arrangement in a standard game of Tetris (if you happen to get the right order of pieces and you place them appropriately). Notice that all of the pieces are ...
7
votes
2answers
354 views

Identical-Looking Keys on a Ring

The number of keys on your key ring has been growing steadily over time, and now you already have 15 keys to keep track of! Unfortunately, you are unable to distinguish one key from another (apart ...
6
votes
2answers
405 views

A construction on an infinite 2d grid, part 1

Recall the classic old problem where we're asked whether a line segment of specific length can be constructed with compass and straightedge, given an initial line segment of length 1? We're going to ...
0
votes
1answer
134 views

Combining parts to make an square

In the following picture, if one puts some of the shapes A, B, C, D, and E together, they can make a square. Then which shapes would be redundant? Only A Only D Only E A and D Can you construct the ...
1
vote
1answer
529 views

Stepladder Puzzle 2: Edge surfing

Continuing the Stepladder Game puzzle series, here's Stepladder Puzzle 2: Edge Surfing If you haven't played the Stepladder Game* before, you should first take a look at the rules, which can be ...
4
votes
2answers
200 views

Stepladder Puzzle 2: Edge Surfing (small target version)

Continuing the Stepladder Game puzzle series, here's Stepladder Puzzle 2: Edge Surfing (small target version) If you haven't played the Stepladder Game* before, you should first take a look at the ...
13
votes
2answers
563 views

Stepladder Game, Introduction and Puzzle 1: Turning

I want to introduce a new game to PSE: the Stepladder Game!* * You may already know this game by another name. The rules for the Stepladder Game: The game is played on a grid. Our grid is ...
10
votes
2answers
316 views

Create a 1 meter measure

How many folding steps do you need to create a $1 \, \text{m}$ measure from an ideal DIN A0 sheet? This sounds easy, but consider that this paper has edge lengths of $\sqrt[4]{2} \, \text{m}$ and $\...
6
votes
4answers
442 views

Constructing 0.35 Unit Length

The Problem The medieval equivalent of Bob the Builder has a new job offer: He is to build a box with the measures of $0.35$ units by $0.35$ units by $0.35$ units for a king. There is a little ...
6
votes
2answers
412 views

How many function blocks do you need to make a controller?

You have 8 binary input signals to a controller, each one for each of the digits 1 - 8. The output is four binary signals, that make up the same number as the input. If the first input signal is ...
9
votes
1answer
174 views

Constructing Tortuous Tours

We'll define a tour of some N x M grid as any sequence of tiles such that the first tile is the bottom left corner, any two consecutive tiles are adjacent, and every tile appears in the sequence ...
-1
votes
2answers
245 views

Robbers - The ultimate compass challenge [closed]

Please read the Cops post for all details. Points are scored on the basis of how long a challenge remains unsolved before you solve. You may solve any number of challenges. You cannot solve your own ...
0
votes
2answers
356 views

Cops - The ultimate compass challenge [closed]

Based on The square and the compass This is a new kind of challenge proposed on Meta Puzzling SE. Any discussion about the general type of puzzle (rather than this particular one) can be done there. ...
2
votes
2answers
223 views

The square and the compass II - Midpoints

Based on The square and the compass The rules are almost the same. (The only difference is the actual task, marked in bold.) You have a compass and a pencil but no scale/straightedge. Your job is ...
6
votes
1answer
508 views

The square and the compass

(I don't mean $x^2$ or $N\cdot S\cdot E\cdot W$) You have a compass and a pencil but no scale/straightedge. Your job is to mark four points on a plane paper that would form a square if joined. Your ...
2
votes
1answer
206 views

Compass-and-straightedge construction of two segments, given their arithmetic and geometric means

Given two segments, construct, using compass and straightedge, two other segments such that the lengths of given segments represent arithmetic and geometric means of the lengths of constructed ...
20
votes
3answers
1k views

The 5040 Square

Fill a $4\times4$ grid with positive integers so that: Every cell has a different integer The product of the numbers in each row is $5040$, and similarly for the columns Source: This was an NPR ...
5
votes
2answers
645 views

Planning an Archipelago

We can place S and Z tetromino shaped islands on an 8x8 grid of water in such a way that no two islands are touching by their edges, because then they would not be two islands. Two islands may touch ...
20
votes
9answers
2k views

Occupy a field with tetrominos

You have a square 8x8 board, and tetrominoes of all possible shapes. Each individual square on a tetromino is the same size as one square on the board (i.e. any given tetromino will cover exactly 4 ...