Questions tagged [construction]
A puzzle that requires an example to be built that fits certain criteria.
56
questions
3
votes
2answers
87 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
169 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 ...
18
votes
1answer
895 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
235 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
142 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
503 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
534 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
208 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
281 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
411 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 ...
6
votes
1answer
362 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
568 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
409 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
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 ...
5
votes
2answers
374 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
169 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
524 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
369 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
694 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
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 ...
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 ...
13
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
387 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
220 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
187 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
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?
12
votes
3answers
305 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
340 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
397 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
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 ...
1
vote
1answer
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 ...
4
votes
2answers
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 ...
13
votes
2answers
550 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
311 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
434 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
410 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
171 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
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 ...
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.
...
2
votes
2answers
216 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
496 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
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 ...
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
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 ...
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 ...
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 ...
5
votes
3answers
374 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.
