# Questions tagged [construction]

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

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### 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 ...
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: ...
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 ...
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 ...
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 ...
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 ...
564 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 ...
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 ...
361 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)...
942 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 ...
549 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 ...
296 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 ...
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 ...
308 views

249 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 ...
134 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 ...
148 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?
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.
205 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,...
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 ...
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 ...
151 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 ...
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 ...
361 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 ...
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 ...
194 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 ...
247 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 ...
522 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 ...
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 ...