# Questions tagged [construction]

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

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### 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 ...
518 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 ...
199 views

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,...
274 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.
405 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 ...
350 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 ...
559 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 ...
328 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? ...
148 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 ...
370 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 ...
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 ...
519 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 ...
359 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)...
686 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 ...
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 ...
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 ...
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 ...
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 ...
367 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 ...
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: ...
218 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 ...
186 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 ...
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 ...
147 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?
289 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 ...
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 ...
386 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 ...
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 ...
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 ...
198 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 ...
541 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 ...
304 views

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 ...
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 ...
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 ...
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.
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 ...
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 ...
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 ...