Questions tagged [solvability]

A question about how a puzzle can be solved.

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56
votes
4answers
63k 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 ...
33
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7answers
17k 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 ...
28
votes
2answers
5k 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 ...
25
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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 ...
22
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2answers
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 ...
17
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4answers
4k 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 ...
16
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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 created ...
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 ...
16
votes
1answer
13k 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
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4answers
13k 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?
15
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4answers
37k 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, ...
15
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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
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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 ...
14
votes
3answers
755 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 ...
14
votes
2answers
863 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 ...
13
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4answers
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 ...
13
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4answers
5k 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 ...
12
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3answers
8k 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 ...
11
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1answer
2k 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 ...
10
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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 top left. ...
10
votes
1answer
338 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 ...
8
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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 ...
8
votes
5answers
2k 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 ...
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 ...
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 ...
8
votes
1answer
386 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 ...
7
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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 ...
7
votes
2answers
374 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 ...
7
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4answers
255 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 ...
6
votes
3answers
29k 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 ...
6
votes
2answers
674 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 ...
6
votes
2answers
492 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 ...
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 ...
5
votes
2answers
650 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 ...
5
votes
1answer
339 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 ...
5
votes
1answer
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). ...
5
votes
1answer
102 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 ...
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
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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
577 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 ...
4
votes
3answers
333 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 ...
4
votes
1answer
283 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 ...
4
votes
1answer
351 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 ...
4
votes
1answer
291 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 ...
3
votes
2answers
361 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 ...
3
votes
4answers
391 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 ...
3
votes
1answer
422 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 $m$ ...
3
votes
2answers
820 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. ...
3
votes
1answer
173 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 ...
3
votes
1answer
106 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 ...