Questions tagged [solvability]

A question about how a puzzle can be solved.

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0answers
122 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?
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4answers
304 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.
3
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0answers
75 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 ...
2
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1answer
109 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 ...
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1answer
103 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....
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1answer
123 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 ...
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4answers
3k 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 ...
2
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2answers
239 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 ...
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5answers
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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 ...
3
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1answer
109 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 ...
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2answers
829 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. ...
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4answers
395 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 ...
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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 ...
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4answers
257 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 ...
3
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1answer
176 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 ...
2
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1answer
120 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 ...
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2answers
678 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 ...
2
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2answers
144 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
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1answer
162 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 ...
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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 ...
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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 ...
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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
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1answer
158 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 ...
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3answers
792 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 ...
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1answer
168 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 ...
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4answers
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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. ...
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1answer
229 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 ...
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2answers
593 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 ...
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3answers
336 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 ...
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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 ...
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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....
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1answer
373 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 ...
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0answers
202 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 ...
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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 ...
14
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2answers
916 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 ...
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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 ...
33
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7answers
18k 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 ...
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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, ...
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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 ...
8
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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 ...
17
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1answer
17k 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 ...
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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 ...
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4answers
66k 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 ...
13
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4answers
6k 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 ...
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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 ...
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2answers
314 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 ...
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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 ...
4
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1answer
293 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 ...
4
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1answer
288 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 ...
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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 ...