# Questions tagged [solvability]

A question about whether a puzzle can be solved.

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3 votes
1 answer
183 views

### "Tape-Nonogram" problem [duplicate]

A Nonogram intro (Credit to Wikipedia for quote) Nonograms, also known as Hanjie, Paint by Numbers, Picross, Griddlers, and Pic-a-Pix, and by various other names, are picture logic puzzles in which ...
0 votes
1 answer
139 views

### Does every validly posed Sudoku have at least one solution and if not what is the minimum number of givens for it to be unsolvable? [duplicate]

Does every validly posed Sudoku (doesn't break any Sudoku rules so only no duplicate 1 to 9 in rows, columns or square) have at least one solution, and if not, what is the minimum number of givens for ...
• 213
2 votes
1 answer
161 views

### Puzzle on a Rubik's Cube

The puzzle is as follows: Consider a solved Rubik's cube. Apply the move sequence M2 U M2 U2 M2 U M2 (Commonly known as the H-permutation in the cubing community). Is it possible to solve the cube ...
16 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 ...
• 69.3k
6 votes
0 answers
639 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
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 ...
• 6,569
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
8 votes
1 answer
427 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
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&...
1 vote
0 answers
172 views

### Are there Sudokus that are so hard that no known logical deduction techniques can reduce it? [duplicate]

Are there Sudokus that are so hard that no known logical deduction techniques can reduce it? Maybe such a technique would reduce away multiple options?
3 votes
0 answers
99 views

### Methods to produce solvable deals in Klondike-solitaire?

About 20% of Klondike-solitaire deals are not solvable. My question is what are the best methods to produce only solvable deals? I thought about two options: Deal a random permutation, then try to ...
• 131
3 votes
1 answer
155 views

### Is this wire puzzle correctly assembled?

I was given this puzzle some years ago and have never found the solution. Recently I picked it up again and have been trying for days to solve it. I presume that the goal is to remove the ring on the ...
0 votes
1 answer
240 views

### Can a 10*10 binary puzzle have more than 1 solution? [closed]

I was trying to solve 10*10 binary puzzle and when I checked with the answer given in the book, the solution in it was different from mine. I did not repeat 1 or 0 more than twice in any row or column....
5 votes
1 answer
142 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 ...
2 votes
4 answers
526 views

### Can someone solve this sudoku without trial and error?

I'm stuck on this sudoku. If anyone can solve this, then please share and explain the method that you used.
2 votes
2 answers
346 views

### Logical Sudoku - How to tell when fully deducted?

I'm working a program that should generate bad ass sudoku puzzles. Recently I noticed there's a thing called "logical sudoku", which means it can be logical-deducted all the way to solution. The ...
• 163
3 votes
1 answer
169 views

### Reapply *some* stickers on scrambled cube

I have this weird cube which have some pieces printed on the plastic and some are detachable. The cube was scrambled not solved and it fell on the floor being cheap cube almost all detachable faces ...
6 votes
2 answers
552 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:
8 votes
5 answers
6k 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
3 votes
4 answers
407 views

### Help with a sudoku puzzle

I would really appreciate some help because I spent more than hours finding another number. It is supposed to be a very hard one but I started well and according to the key, my numbers are correct. Do ...
• 207
7 votes
4 answers
278 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
3 votes
1 answer
190 views

### Stuck on (a couple of) diagramless kakuros

I was working through OAPC 6 (http://oapc.wpc2009.org/archive.php?id=46). I was having trouble with the diagramless kakuros. The rules for this puzzle are as follows: Place the numbers $1-n$ (7 and 9 ...
• 147
2 votes
1 answer
138 views

### Does the puzzle have a unique solution?

Let's say you have a sphere-maze. The sphere is fixed on the fixed half-ring (1) and two independent rings (2) and (3). These rings are connected at point A. Inside the sphere one can see a small ...
• 1,691
6 votes
2 answers
691 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
3 votes
2 answers
195 views

### Stuck on a Tapa (variation)

I am stuck on a Tapa puzzle. I have tried solving it a number of times and keep running into the same problems. I am starting to wonder if it is solvable at all. As far as the puzzle itself goes, best ...
• 147
2 votes
1 answer
183 views

### What can be the next move without guessing in this almost solved Sudoku puzzle?

I am currently stuck at this puzzle where I can't think of the next move without guessing it. I was surprised to be in this situation after solving ~70-80% of the puzzle. I thought for all possible ...
• 125
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
2 votes
1 answer
209 views

### How to solve this Rubix cube? [duplicate]

Help!!!! Is this rubix configuration solvable? These are the only two pieces in the wrong place. If the answer is no, what pieces do I need to reconfig to make the cube solvable? Note that my kid ...
1 vote
1 answer
494 views

### Misaligned Cube: How to fix? [duplicate]

There must have been an accidental turning of corners. Now, I do not know how to turn corners, so that the cube is solvable again. The red and blue edges are the only misaligned pieces.
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 ...
• 114k
7 votes
1 answer
324 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.
• 133
0 votes
1 answer
203 views

### I don’t know how to solve the last pieces

So, I almost finished a rubik’s cube, but the last 3 pieces are not in their places (green on red face, blue on green face, and red on blue face). Apart from these, the other faces are done. How can ...
2 votes
1 answer
268 views

### Fixing a Binairo Mistake

The rules of Binairo are simple: 1) Each row and column must have an equal number of black and white circles. 2) There can be no horizontal/vertical line of three like-color circles. Starting ...
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
4 votes
3 answers
363 views

### Anyone know of an impossible, trick puzzle? [closed]

My dad really likes mechanical puzzles and has drawers full of them to show to people. My family has decided that it would be a great joke to find a new one that he hasn't seen, that is actually ...
• 43
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 ...
• 3,674
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
1 answer
524 views

### Is solving a puzzle using uniqueness invalid? [duplicate]

(I don't know if this is appropriate to ask here, since it's a bit of a soft question about puzzles, rather than a puzzle itself. I'm not certain about the tags either.) When I was first introduced ...
• 153
1 vote
0 answers
225 views

### I'm not able to solve any of these puzzles. How can I get started? [closed]

I'd really like to solve a puzzle but I can never see any pattern or anything. Is there something that can teach me? I've also read about being familiar with puzzle types but I don't even know how to ...
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
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 ...
• 7,224
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 ...
3 votes
2 answers
367 views

### Tony Horncastle's number

When Tony Horncastle wakes up, and sees the digital clock, he need to reach that number using 75, 25, 1, 3, 5, 7. For example, 4:37 could be (75 - 3) x (7 - 1) + 5. Tony believes that there is ...
• 1,143
13 votes
4 answers
7k 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 ...
• 17.8k
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 ...
• 1,670
4 votes
1 answer
301 views

### What is guessing? [closed]

The whole difficulty of solving puzzles like sudoku is doing it without guessing. Well, either without any guessing whatsoever or with little enough that a human can still make retractions and come to ...
• 187
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. ...
• 114k
4 votes
1 answer
305 views

### Can the rook pass every square just once?

I had a math teacher in high school who gave us a puzzle to solve. We had to draw a chessboard with one piece that could only move in straight paths. Diagonal movement was forbidden. The goal was to ...
• 59
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 ...
• 9,722
0 votes
2 answers
946 views

### Connect the Dots Problem

Using the image above, the rules are every dot must have a line through it, no diagonal lines, no crossing over lines, no backtracking, no going out of bounds, and no picking up the pencil to start at ...