Questions tagged [solvability]
A question about whether a puzzle can be solved.
83
questions
61
votes
2
answers
7k
views
Does the Rubik's Cube in this painting have a solved state?
This is an image of a Rubik's Cube I found in the Men's Toilets during the first day of a big Scrabble tournament.
This position is impossible for the standard Rubik's Cube (White/Red/Blue opposite ...
- 7,444
60
votes
4
answers
83k
views
What is the maximum number of solutions a Sudoku puzzle can have?
I've seen Sudoku puzzles that can be solved two different ways. Referring to a traditional 9x9 grid:
Is it possible for a Sudoku puzzle to have more than two solutions? If so, what is the maximum ...
- 2,393
33
votes
7
answers
24k
views
Why does the 4x4 Rubik's cube have parity cases, while the 3x3 does not?
I'm a little uncertain as to why these two parity situations occur on the 4x4 Rubik's cube. The first parity case that can occur is this one, where an edge is simply flipped upside down:
The ...
user20
29
votes
11
answers
4k
views
Is there a puzzle that is only solvable by assuming there is a unique solution?
Is it possible to construct a puzzle that is:
Solvable if you assume there is a single unique solution
Not solvable if you do not make this assumption
My intuition says that the answer is "No&...
- 409
29
votes
2
answers
6k
views
Does this metal puzzle have a solution (Baguenaudier)
When I was young I got this puzzle as a gift to me.
The aim is to get the long piece out. I haven't yet found a solution, and I'm not sure if there is one
Does this have a solution and if so ...
- 393
26
votes
5
answers
2k
views
Polyomino T hexomino and rectangle packing into rectangle
Let's pack some (one or more) T hexominoes together with some (one or more) small $a\times b$ rectangles into some bigger $m\times n$ rectangle without holes and overlapping pieces.
For example, I ...
- 1,018
23
votes
2
answers
3k
views
Is this "Gear Turning" puzzle on Puzzlopia always solvable?
I have recently started to spend time on http://www.puzzlopia.com/ (EDIT: Site is now dead, see here: https://web.archive.org/web/20161007014010/http://www.puzzlopia.com/), which is a puzzle site. If ...
- 9,892
20
votes
4
answers
6k
views
Alphametic (Verbal Arithmetic) general strategy
According to Wikipedia, Alphametics, also known as verbal arithmetic, can be defined as "a type of mathematical game consisting of a mathematical equation among unknown numbers, whose digits are ...
- 3,602
17
votes
4
answers
3k
views
Strategy for finding the key to this cipher
A coworker and I are perplexed over this puzzle. We gave up and looked at the answer, but we cannot seem to understand how it works. Can anybody explain?
Text version of the above image
We've created ...
- 171
17
votes
3
answers
4k
views
Barely Illegal Rubik's Cube State
(If you are not interested in the backstory, you can skip right to the picture.)
At Most Complicated Illegal Partial State of Rubik’s Cube, user @happystar asks a very interesting question about ...
- 75.9k
17
votes
1
answer
20k
views
Tips for solving poem riddles
Poem riddles are becoming more prolific and more popular on Puzzling.SE (examples: Pacoverflow Riddle Poem, Pacoverflow Riddle Poem #2, Identity Crisis: What Am I?).
Inspired by the 'Tips for Golfing ...
user2174
17
votes
4
answers
1k
views
How many possible starting positions are uniquely solvable for a nonogram puzzle?
This type of puzzle goes by many names: Nonogram, Picross, and Griddlers are all mentioned on the Wikipedia page, Simon Tatham calls it Pattern, I was introduced to it as Descartes Rainbow, ...
The ...
- 116k
16
votes
5
answers
2k
views
Should the angels play their game?
Two angels in heaven want to play a game. One of them comes up with an arbitrary, computable function from the integers to the integers. The other angel has to guess what it is. The second angel can ...
- 1,273
16
votes
4
answers
44k
views
Is it possible to use one sequence of moves to solve the Rubik's cube from any position?
Is there a sequence of moves that can be repeated over and over again which can solve any legal position the Rubik's Cube? If so what is it, and if there's more than one, what's the shortest? If not, ...
- 14.4k
16
votes
4
answers
17k
views
Fast strategies for solving Einstein's puzzles?
The Einstein's puzzle or zebra puzzle is a well-known logic puzzle. Are there any very easy ways to solve it fast?
- 661
16
votes
3
answers
2k
views
Are there any popular puzzles with polynomial-time algorithms?
First, a little background: as I noted in my answer to another question here, most of the puzzles that seem to stay popular for extended periods of time are canonically 'hard' in an algorithmic sense: ...
- 2,481
15
votes
2
answers
2k
views
Hotaru Beam Puzzle: Is it impossible?
I saw this puzzle on Twitter by user @lilva_0419 and I personally feel that it is impossible to solve. Can you prove me wrong (or right)?
Source on Twitter
Try it online
Rules (see Wikipedia):
...
- 273
14
votes
4
answers
4k
views
Solving "odd one out" problems. What am I doing wrong?
I find I do very badly at word based odd-one-out-type puzzles. It generally seems to be the case (at least, in my experience) that almost any of the items can be chosen as the odd one out, and this ...
14
votes
2
answers
2k
views
How to solve elastic band puzzles?
There was a Puzzle competition last weekend, in which there were a couple of puzzles titled "Elastic bands".
Fill in each circle with a letter so that the two networks are identical; that is, if ...
- 7,262
14
votes
2
answers
2k
views
Does this grid puzzle with a symmetry-breaking condition have a solution?
Since challenge questions are up in the air, what better time to pose a puzzle-building question that's intrigued me for some time.
Preamble
Consider an infinite square grid made up of nodes and edges ...
- 10.1k
13
votes
4
answers
9k
views
Strategies for solving steganography puzzles
I've seen a lot of puzzle here tagged steganography but I mostly ignored them for now because I have no idea on how to even approach these.
The past days, I tried to read the answers to some of them ...
- 17.9k
13
votes
1
answer
4k
views
General strategies for solving metal disentanglement puzzles
(When I talk about metal disentanglement puzzles, I have in mind Hanayama and Tavern puzzles.)
As opposed to twisty puzzles - which I can approach by playing with commutators and conjugates as a way ...
- 315
12
votes
3
answers
9k
views
Rubik's cube without any algorithms
I am learning to solve a Rubik's cube using some algorithms (I don't completely understand why they work). I had a Rubik's cube when I was little and I remember solving it 2-3 times without using any ...
- 375
12
votes
1
answer
78k
views
How to solve this 3D wooden puzzle which becomes an interlocking cross?
I got a 3D wooden puzzle in which you are supposed to rebuild. I took pictures of the 6 pieces (click images to enlarge):
I found this image on the Internet. I believe it's the solved version:
How ...
- 14.4k
10
votes
4
answers
2k
views
JonMark Perry's Grid Logic Puzzle
Consider the following puzzle type proposed by JonMark Perry.
Start with a square grid of arrows, each one pointing in one of the four cardinal directions. For example:
You start at the top left. ...
- 116k
10
votes
4
answers
1k
views
Tips for solving this puzzle (ring, wood and string)
After 10 years and many, many hours spent on this puzzle, I'm slowly seeing it worn out more and more. I'm completely stuck and whenever I pick this up again I end up doing the same that I've already ...
- 109
10
votes
1
answer
370
views
Web of Spirits - a puzzle of romance
Spirit Web:
Can you figure out the interconnected web of affections among these characters using the provided clues?
Basic Rules:
1: There are exactly three existing relationships.
2: No character in ...
- 3,909
9
votes
5
answers
1k
views
Polyomino Z pentomino and rectangle packing into rectangle
See my similar question about T hexomino (Polyomino T hexomino and rectangle packing into rectangle)
This is exactly same but with other polyomino - Z pentomino.
Let's pack some (one or more) Z ...
- 1,018
8
votes
5
answers
10k
views
Best way to solve Codeword puzzle
I always find it hard to do codewords puzzles. Whenever I fill in all the spaces with the starting letters, it doesn't really help. I always end up looking at the answer sheet.
Does anybody know a ...
- 399
8
votes
2
answers
2k
views
Stuck on a puzzle
I have been working on a Knapp Daneben Tapa, where each clue is wrong by exactly one unit. I have tried it a few times and keep running into the same problem. I think I am solving it deductively/not ...
- 147
8
votes
2
answers
3k
views
Can you solve the 7x7 (sudoku-ish) centered sums puzzle
I have come across this puzzle a few times in competitions and rally's, and it has troubled me because I cannot seem to find a good approach to solving it, either programmatically or numerically. And ...
- 183
8
votes
1
answer
628
views
What is the name & solution for this 33-piece 3D wooden puzzle?
I purchased this 3D wooden puzzle and wasn't provided with the instructions to reassemble it. I can't seem to find any information about it other than the source I bought it from.
It has 33 pieces
...
- 191
8
votes
2
answers
4k
views
How to solve this wood/string/ring puzzle
When I was living in Argentina, I encountered this puzzle:
I believe the goal is to somehow free the string so it only passes through the small hole in the side (at the right in this image; somewhat ...
- 183
8
votes
1
answer
404
views
Visualise Whirled Peas
My eldest came home with some interesting maths homework.
We have three bowls containing peas.
Distribute the peas evenly across the bowls, by moving peas from one bowl to another. The only ...
- 5,088
7
votes
2
answers
505
views
Fill up a tetris field where bordering tiles have different colors
Is it possible to completely fill the infinite tetris field $\mathbb Z^2$ with tetrominoes such that no tetromino borders another one of the same type?
Assume that two tetromiones border each other ...
- 13.5k
7
votes
2
answers
2k
views
Number sequence solving strategies
Number sequences are one of the oldest puzzle categories in the book. You would find it hard to look through a days worth of puzzles posted here and to not find any puzzles that involve some sort of ...
- 3,699
7
votes
3
answers
5k
views
Does AAA+BBB+CCC+DDD=ABCD have a solution for distinct digits A,B,C,D?
I was asked to solve the following sum:
AAA
BBB
CCC
DDD
--------
ABCD
What I managed to found is that ...
- 1,156
7
votes
1
answer
351
views
$4\times4\times4$ Rubiks cube Top Layer Issue
The only way i am able to solve is to jumble the whole cube again. If you know the way to solve pls give images or algorithm.
- 143
7
votes
4
answers
285
views
Christmas Sentences
I've received an early Christmas gift with a combination lock and a letter containing a poem and some sentences. There are several typos: I don't believe they're intentional, but they might be. I have ...
- 171
6
votes
3
answers
31k
views
Solving Rubik's cube with one algorithm [duplicate]
I was wondering if it's possible to solve a Rubik's cube just iterating a single algorithm. It doesn't matter how complex the algorithm is (as long as it is less than 1 million moves), nor the time ...
- 12.6k
6
votes
2
answers
700
views
Is there a way in which all the members can be seated?
Here's a puzzle where it is very difficult to find a possible seating arrangement of all the members.
I have been struggling to solve it. I have devoted so much of my time trying to figure out ...
- 323
6
votes
3
answers
2k
views
Does the last row of a N x N sliding puzzle need to be solved?
If I successfully arrange all the blocks of every row of a sliding puzzle except the last row in proper order, will the n-th row be automatically resolved? (Assuming that the puzzle is solvable in the ...
- 63
6
votes
2
answers
763
views
Metal puzzle - Spiral and Triangle with U-Shape; Triangle with Ring at the beginning
I got the puzzle from here. Here is a picture of it:
How is it possible to solve it?
UPDATE: Thanks @JaapScherphuis - this is the solution:
- 63
6
votes
0
answers
905
views
Name and solution of puzzle to rotate all arrows to same direction
In this puzzle, when you click an arrow, all arrows immediately next to it (diagonally included), as well as the arrow you clicked itself rotate 90 degrees. The goal is to get all the of arrows to ...
- 61
5
votes
2
answers
716
views
What to do when the official Rubik's cube solving sequence breaks?
So, the official guide shows you exactly how to solve the white cross, first layer, etc. but on the second layer, assume you've completed every little square but one (and edge) and that there's 2 ...
- 14.4k
5
votes
2
answers
1k
views
Solutions for generic polyomino puzzles
Inspired by Mosaic with tetris blocks I was wondering if there were any generic algorithms to solve or show there was a solution to these types of problems (i.e. placing polyominos on a 2D board).
...
- 1,151
5
votes
1
answer
386
views
Alberi Puzzle, no idea where to go
The following image is a puzzle I've been stuck in for about a week now, I was wondering how to go about solving it:
The way it works is that any given row, any given column and any given area has ...
- 7,756
5
votes
1
answer
153
views
Competitive puzzles
Do you know any sort of puzzles that can work in the context of a short competition? In other words, puzzles that have these features:
The premise should be fairly simple to follow (but the solution ...
- 151
4
votes
1
answer
1k
views
Is there an efficient algorithm for solving tiling puzzles?
As an example of the type of problem, consider Stewart Coffin's Cruiser puzzle:
Let R be a 48 × 31 rectangle. Let T be a 30°-60°-90° triangle with
hypotenuse 34.565 (so legs are 17.2825 and 29....
- 363
4
votes
5
answers
1k
views
Systematically solving a certain logic puzzle: win prize B when the truth of your statements relates to prize A
I came along this puzzle somewhere it a logic-related lecture:
There are two prizes: Prize A and prize B.
When you make a true statement, then you win prize A.
When you make a false statement, then ...
- 1,690