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Questions tagged [construction]

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

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32
votes
12answers
4k views

Mr. Hilbert and the Problem of the Erroneous Equation

Having had just checked into the Grand Hotel, Mr. Hilbert slumped into the hotel room armchair with relief. Finally he could have some peace and quiet and solve the quaint riddle his colleague gave ...
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: ...
25
votes
1answer
2k views

Create a Word Search

Create a word search with the following conditions: Use the eleven words below. They can be spelled up, down, left, right, or any of the 4 diagonal directions. ZERO ONE TWO THREE FOUR ...
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 ...
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 ...
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 ...
14
votes
4answers
556 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 ...
13
votes
4answers
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 ...
13
votes
2answers
358 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)...
13
votes
2answers
928 views

Devising a sudoku where the rows are the moves for a draw in tic tac toe

The task is to construct a sudoku whose rows (or columns) are the moves for a game in tic tac toe where the game ends in a draw. Here are some clarifications and constraints which should limit ...
13
votes
2answers
538 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 ...
12
votes
3answers
280 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 ...
11
votes
1answer
2k views

Building towers with colored blocks

You have blocks in five colors (red, green, yellow, blue and black - or 1 to 5). Each color comes in two varieties: a cube and one as big as two cubes stacked atop each other (sizes 1 and 2). You are ...
9
votes
2answers
303 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 $\...
9
votes
1answer
470 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 ...
9
votes
2answers
517 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 ...
9
votes
1answer
170 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 ...
8
votes
3answers
363 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 ...
7
votes
2answers
269 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.
7
votes
2answers
317 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? ...
7
votes
2answers
333 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 ...
7
votes
2answers
214 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 ...
6
votes
1answer
682 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 ...
6
votes
1answer
517 views

Chess Construction Challenge #2-Check!

Xit's time for round two! Given that: -Black has 6 pawns and a king -White ehas three pieces of any kind you to deduce the identity of and a king Construct: -A nlegal position in which both sides ...
6
votes
1answer
488 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 ...
6
votes
2answers
380 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 ...
6
votes
4answers
433 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
1answer
340 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 ...
6
votes
2answers
396 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 ...
5
votes
2answers
643 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 ...
5
votes
1answer
404 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 ...
5
votes
2answers
367 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
168 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 ...
5
votes
2answers
246 views

Brave Knight's Journey in N Dimensions

Queen Shayra does not have the most impressive following, but she intends to expand her influence. If she could settle down at the center of an N Dimensional 3-Cube and build a palace there, she would ...
5
votes
1answer
145 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?
5
votes
3answers
372 views

Square inscribed in a circle (with a ruler only)

Inscribe a square in a given circle by following the rules of construction with ruler and compass but... without using the compass. The center point of the circle is given too.
4
votes
2answers
196 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,...
4
votes
2answers
196 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 ...
4
votes
1answer
216 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 ...
4
votes
1answer
146 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 ...
3
votes
1answer
135 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 ...
3
votes
1answer
360 views

Create a Homophone Word Search

This recent puzzle I created was well-received, so here's another one like it, except this time a bit larger and using homophones. Create a word search with the following conditions: Use the fifteen ...
2
votes
2answers
215 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 ...
2
votes
1answer
192 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 ...
1
vote
1answer
245 views

Find the optimal dot configuration

Rules: You have 9 dots, labeled A through I. You choose a layout (arrangement) for the 9 dots. You must connect the 9 dots with straight lines (no curves or extra lines). The object is to ...
1
vote
1answer
521 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 ...
0
votes
1answer
133 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 ...
0
votes
2answers
354 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. ...
-1
votes
2answers
185 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 ...
-1
votes
2answers
244 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 ...