# Questions tagged [solvability]

A question about whether a puzzle can be solved.

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### 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 ...
1k 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 ...
1 vote
174 views

### Impossible Minesweeper?

I was playing the game Minesweeper earlier today and came across the following situation: (Look at the bottom-middle section of the gameboard.) It seems to me that either of the two diagonal pathways ...
453 views

### Beach Umbrellas puzzle: did I make a mistake or is Brainzilla wrong?

https://www.brainzilla.com/logic/logic-grid/beach-umbrellas/ has the following puzzle: Four families are going to the beach in the morning and are bringing their family-size umbrellas. Which family ...
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: ...
13k 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 ...
1k views

### Wooden disentanglement puzzle

I recently came across this disentanglement puzzle and after spending weeks trying to understand and solve this seemingly simple puzzle, I am completely stumped. I do not know what the end goal of ...
678 views

### Possible parity for sliding puzzle

As you can see, I have a sliding 5x5 puzzle, but no matter what way I scramble it and solve it again, I always seem to have two pieces that need to be swapped. Is there a way to swap the two pieces? (...
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 ...
221 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 ...
2k 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 ...
366 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.
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 ...
1 vote
1k 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.
277 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 ...
255 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 ...
187 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 ...
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&...
85k 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 ...
2k 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). ...
197 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 ...
45k 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, ...
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 ...
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 ...
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 ...
213 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 ...
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): ...
939 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:
5k 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 ...
84k 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 ...
756 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 ...
1 vote
193 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?
739 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.
155 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 ...
283 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 ...
388 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....
158 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 ...
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 ...
435 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 ...
927 views

### Unsolvable sudoku net with maximum blocks

Definitions For a $9\times9$ grid $G$ (not necessarily respecting sudoku rules), a subset of cells $S$ is defined to be sudoku-friendly if the values in $S$ do not contradict the rules of sudoku. ...
414 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 ...
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 ...
288 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 ...
206 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 ...
155 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 ...
703 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 ...
202 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 ...
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 ...