# Questions tagged [solvability]

A question about whether a puzzle can be solved.

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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Line(ish) puzzle [closed]

Is it possible to connect the opposite numbers (2 and 4, 1 and 3) simultaneously? If not, give me an explanation. Rules: 1. You can use any shape. (Torus, Möbius loop, etc.) 2. You can use any ...
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 ...
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### 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 ...
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1 vote
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### Check sudoku solvability

With a blank grid, I put and number (1-9) any cell, the Sudoku has n solutions. I continue filling any blank cells with numbers that satisfy the constraints, so the Sudoku still has many solutions, ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
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### Is there a solvable 2-box Sokoban puzzle in which the pushes must be interleaved?

Say that a solution to a Sokoban puzzle with only 2 boxes is box-isolating if and only if there are step numbers $m$ and $n$ such that for one of the boxes: All of its pushes were between step $m$ ...
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### 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 ...
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### 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 ...
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### Check to see if a Configuration is Possible: prove there's an Hamiltonian path on a connected subset of the square grid graph

Alright, here's a new one for you guys. Instead of solving it, you need to determine if any given configuration is possible to solve, without actually solving it. It needs to be a general method of ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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). ...
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### 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, ...
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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 ...
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### 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 ...
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### 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 ...
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### 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: ...
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### 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?
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### 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 ...
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