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Questions tagged [solvability]

A question about how a puzzle can be solved.

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2
votes
2answers
120 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 ...
2
votes
1answer
140 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 ...
8
votes
2answers
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 ...
2
votes
1answer
110 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 ...
12
votes
3answers
609 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 ...
0
votes
1answer
154 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
1answer
190 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 ...
3
votes
3answers
319 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 ...
6
votes
2answers
272 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 ...
4
votes
1answer
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....
4
votes
1answer
224 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 ...
1
vote
0answers
174 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 ...
11
votes
1answer
1k 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 ...
14
votes
2answers
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 ...
12
votes
3answers
2k 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
2answers
356 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 ...
13
votes
4answers
4k 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 ...
4
votes
5answers
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 ...
4
votes
1answer
275 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 ...
10
votes
4answers
1k 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 ...
3
votes
1answer
261 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 ...
21
votes
2answers
3k views

Is this “Gear Turning” puzzle on Puzzlopia always solvable?

I have recently started to spend time on http://www.puzzlopia.com/, which is a puzzle site. If you are not logged in, you are greeted with a "gear turning" puzzle, where you want all the "gears" ...
0
votes
2answers
264 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 ...
8
votes
2answers
2k 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 ...
7
votes
3answers
3k 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 ...
10
votes
1answer
323 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 ...
5
votes
1answer
323 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 ...
6
votes
2answers
343 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 ...
-6
votes
4answers
144 views

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 ...
27
votes
2answers
4k 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 ...
12
votes
3answers
7k 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 ...
1
vote
1answer
5k views

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, ...
8
votes
1answer
367 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 ...
16
votes
4answers
2k 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 ...
6
votes
3answers
1k 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 ...
3
votes
2answers
752 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. ...
6
votes
3answers
27k 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 ...
3
votes
1answer
405 views

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 $m$ ...
16
votes
5answers
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 ...
8
votes
5answers
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 ...
4
votes
1answer
550 views

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 ...
14
votes
2answers
783 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 ...
5
votes
2answers
637 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 ...
25
votes
5answers
1k 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 ...
5
votes
1answer
994 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). ...
15
votes
4answers
32k 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, ...
32
votes
7answers
15k 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 ...
16
votes
1answer
10k 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 ...
15
votes
3answers
1k 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: ...
14
votes
4answers
12k 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?