Questions tagged [construction]
A puzzle that requires an example to be built that fits certain criteria.
-2
votes
0answers
78 views
-4 to 3 magic square [on hold]
Write the numbers -4 ,-3 ,-2,-1,0,1,2,3 in correct place value so that each of the square adds up to 0
Please solve this question, because I have tried this this question many times without success. ...
5
votes
1answer
393 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
155 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
535 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 ...
6
votes
2answers
243 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
133 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
361 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
149 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 ...
8
votes
2answers
507 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
...
11
votes
2answers
338 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
639 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
214 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 ...
2
votes
1answer
133 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
4answers
970 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
308 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
206 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 ...
-2
votes
2answers
163 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
118 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
141 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
252 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
313 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
372 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
131 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
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 ...
4
votes
2answers
195 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
520 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 ...
9
votes
2answers
278 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
430 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
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 ...
9
votes
1answer
168 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
241 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
351 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
212 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
478 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
186 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
371 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.
2
votes
1answer
347 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 ...
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
...
1
vote
1answer
242 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 ...
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 ...
5
votes
2answers
245 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 ...
13
votes
2answers
915 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 ...
