# Questions tagged [logical-deduction]

A puzzle that requires formal logical deduction to arrive at the solution. This suggests more than merely reasoning through clues to find an answer (you might want [situation] for that).

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### A signaling problem

There are garrisons of soldiers spaced equally along the borders of the Empire. When the border is attacked, the nearest garrison lights a fire on a large tripod. The distance between garrisons is ...
• 17
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### Painting a Checkerboard

I love checkers - but I've played it so much that the color of my board is faded and dull. Today, I resolved to paint it. Unfortunately, I slipped and fell :( Now there's paint all over my ...
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### Can experienced players tell when a Sudoku was randomly generated? Or if it's a shuffled version?

I'm trying to make a simple classic Sudoku game in JavaScript, and I'm wondering what considerations I should have in how experienced players might interpret the generated puzzles. I'm not very ...
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### Hard Sudoku: hint for next number

I tried a hard sudoku and I can't figure out what the next number is. I tried some online tools without any success (I don't want to have the final solution without any explanation). I would be very ...
739 views

### How to Divide 1,987 Gold Coins Among 40 Pirates?

There are 40 pirates, designated as P1, P2, ...... P40, respectively. They aim to divide 1,987 gold coins using a two-stage division scheme: In the first stage, P1 initially splits all the coins into ...
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### Boulders in Valleys - Magnetic Confinement

This is a "Boulders in Valleys" puzzle - it's been posted a few times on this site. This specific puzzle's solution has an interesting property that made it quite hard to design. The ...
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### Solving this "Who committed the murder" puzzle using truth tables or propositional logic

I'm trying to solve a logic problem, and I'm wondering if it can be done using truth tables or propositional logic. The problem goes like this: Who killed the mouse? The owl said the hawk did it. ...
413 views

### Understanding solution for this puzzle where truth-tellers and liars describe game scores

Source (Page 26-28) Frieda was fond of visiting exotic locations. On her visit to the island of Yippiekaiyay, she was surprised that the natives of the island could be classified into one of two ...
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1 vote
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### Explanation why next cell has to be a certain value

I'm an absolute beginner and was stuck at the first puzzle of Sven's Sudoku Pad. I reached the following board state, where I noted for every cell which values were possible: After a while I simply ...
260 views

### The possibilities keep reducing

You find yourself participating in a thrilling puzzle tournament, prepared for any challenge that comes your way. In front of you, there is a safe. It looks like a large black cube, except for the ...
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### Important Alien Message

A strange alien transcript, alongside what is believed to be a partial key, was recovered the other day. Scientists aren't sure what the message might contain, but theories point to some sort of ...
147 views

### How many earrings do you have to pick up? [closed]

I'm having trouble solving a puzzle in Swedish. I've translated it below: How many earrings do you have to pick up to be sure to get a pair of the same in a mix of earrings where "favorable ...
1 vote
72 views

### Three rows of letters, find the missing letter in row 2 [closed]

Row 1. CGIKNUXY Row 2. ADOQR Row 3. B In row 1, the pattern goes 3421 In row 2, this pattern doesn't work.
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### Need help solving a multiplication puzzle

The puzzle goes as follows: Each letter corresponds to a number, what is the result of the multiplication? RQQ × P ___ QST I'm not sure where to start with this puzzle. I know that each letter ...
1 vote
225 views

### Need help solving the 'Who killed the vole' puzzle - Can you crack the code? [duplicate]

I am hoping to get some help with a puzzle that I've been struggling with. The puzzle is called "Who killed the vole" and it goes like this: There are four birds - hawk, owl, sparrow, and ...
179 views

### Making a large Candy Crush unicolor box

I played the arcade game Klaxxon a lot (comparable mechanics to Candy Crush, long before the latter even existed) and always wondered if I could get a monster super ultra bonus by making a 3 x 3 ...
2k views

### Two Doors and a Guard

While trekking through the swamp of Knights and Knaves, you come upon a pair of doorways: One leading out of the swamp, the other leading to your doom. The swamp of Knights and Knaves is a strange ...
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1 vote
134 views

### Logical puzzle with possibly two answers [closed]

1+8 = 9 2+6 = 14 5+7=40 1+2+11=? I arrived at two possible solutions: 1) 23 by A+(AxB) = answer for previous ones and lastly A+(AxBxC) for last one to find the value of "?". 1+(1*8)=9 2+(2*...
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### The Order of Ptolemy: The Initiation

You enter the room and hear the click of the door behind you. On a stone altar of light marble, there are three small statues overlooking 12 cards laid out in neat rows upon the smooth surface. An ...
1 vote
135 views

### Circuissonne Diagrams

This puzzle is part of the Monthly Topic Challenge #7: Board games. And also, this puzzle is also a parody of XKCD's 730. We're starting a project on Explain XKCD (link currently not available) to ...
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491 views

### Many Moons (and Suns) Ago

This is part 12 of the puzzle series Around the World in Many Days. Each part is solvable on its own. Many moons ago, on an island far, far away… Deаr Puzzling, Today I have a Moon-or-Sun puzzle for ...
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245 views

### Farthest From Backgammon

This puzzle is part of the Monthly Topic Challenge #7: Board games. The famous Backgammon game can be seen as being played on a number axis with one player on the non-negative side (from 0 to 25) and ...
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704 views

### Mind Reading in Three-Handed Pot Limit Omaha

Alice, Bob, and Charlie are playing a game of Pot Limit Omaha. After the river card is dealt, but before the players' hands are revealed, the following conversation takes place: Alice: "My hand ...
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### What's the next step to solve this Nonogram?

I've gotten myself stuck in this Nonogram level using the logic I'm familiar with (filling in our crossing out boxes that will always be filled in or empty no matter how you fill in the grid). And ...
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### Why can't a 1 go in this field

I've moved onto "expert" sudoku's in my app (Sudoku.com on IOS) and whilst I am getting by solving some, others I'm having a hard time with. With this one, I used a hint so the AI could note ...
• 151
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### Sixty-three knights on a chessboard

This puzzle is part of the Monthly Topic Challenge #7: Board games. If we're using rooks, then this would be equivalent to a classic "fifteen puzzle" though on a larger grid. This time we'...
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### Colorblind Mastermind

This puzzle is part of the Monthly Topic Challenge #7: Board games. Inspired by the incident, I created a variant of Mastermind, although it wasn't actually intended for colorblind people. The main ...
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### Are there seven consecutive annual dates which result in Monday-Sunday?

Choose a date that's a Monday, e.g. 1st Jan 2024. Then keep adding 1 year until you have seven dates in a row that are the days of the week in order (Monday to Sunday). Does such a date combination ...
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### Friends and Enemies

Here is a short puzzle I made: There are 10 people arranged in a row, and each of them has a friend and an enemy also present in the row. Your goal is to identify the friend and enemy of each person. ...
1k views

### Next step in this Slitherlink puzzle (Honeycomb)

I have applied all of the techniques that I know of, and can't figure out the next logical step. I even turned on the visual clues, but it didn't help. What would be the next move without resorting to ...
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### The Key to the City

This is part 9 of the puzzle series Around the World in Many Days. Each part is solvable on its own. Deаr Puzzling, This is a Skyscrapers puzzle. Each letter represents a unique number between 1 and ...
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### Two roads, one guard [duplicate]

You are at a crossroad. One road goes to hell, the other to paradise. There is one guard. The guard only answer questions and only using Yes or No. The guard is one of two categories: one category ...
1k views

### Guessing two secret numbers

I thought of two secret numbers $A$ and $B$ that are between $1$ and $10$ inclusive. Each turn you can provide me with your guesses $A'$ and $B'$ and I will tell you the sum of the absolute ...
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### Trust me: you do not want to go down this road with me

Every cell has a digit from 0 to 9 or one of the four operation symbols +, −, ×, and /, signifying addition, subtraction, multiplication, and division respectively. No digit appears more than once in ...
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### How to make gifs showing a puzzle's solution process?

I've been repeatedly asked to turn this into a PSE question, so here goes. Some people may have noticed that, when I answer a grid-deduction question, my answer often includes, as well as a step-by-...
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### Guessing the missing card from the remaining four cards [duplicate]

I was inspired by this beautiful puzzle. Five people sit at a table. Wiske has them each draw a card of their choice from an open standard deck of 52 cards. They show him their card and then lay it ...
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379 views

### "Symmetric" Tetrikabe

This puzzle's theme is inspired by one from Grandmaster Puzzles' "The Art of Puzzles", but the puzzle itself is original. Rules: (Nurikabe section shamelessly stolen from an earlier puzzle ...
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### Good and bad numbers of remaining mines

You've been tasked with finishing solving this Minesweeper board: "How many mines remain?", you ask. "I'm just choosing that now, actually. Tell you what: I was going to consider every ...
502 views

### Boulders in Valleys

This is a "Boulders in Valleys" puzzle (previously called "Balls on Hills"). It's similar to Slitherlink and Corral; your goal is to draw a path along grid cell edges that ...
• 681
636 views

### Happy 2023! Another empty Suguru (Tectonic)

Another assignment for the Suguru (Tectonic) fans out there. Fill in a number in each empty square so that: Each block of n squares has the numbers 1..n. Neighbouring squares are not be equal (...
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577 views

### Balls in Pockets (Balls on Hills)

This puzzle is a "Balls on Hills" puzzle. It's similar to puzzles like Slitherlink in that your goal is to find a curve given some clues. The intuition behind this puzzle is balls rolling ...
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551 views

### Balls on Hills - Loop Deduction Puzzle

This puzzle is a loop deduction puzzle, like Slitherlink and Masyu. It is based on the idea of balls rolling down hills - the clues here give the distance that a ball can roll down. The Puzzle ...
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### How many Nonconsecutive Sudoku solutions are there?

Consecutive Sudoku is a variant with the additional rule that orthogonally adjacent numbers are consecutive if and only if there is a dot/bar on the line between them. A Nonconsecutive Sudoku is one ...
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### Hat guessing without knowing the colors

Generalization of this problem: Guessing hat colors. 4 prisoners Suppose that there are $N$ prisoners, instead of $4$. Show, by finding explicitly the strategy, that if $N$ is even there is a strategy ...
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### Right turn only puzzle

Here is a grid with 24 spaces filled with letters. Pick any place to start your travel in the grid taking right turns only. You must get to all remaining 23 spaces but only once. By doing so create a ...
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### Which sentences in S := {"the number of lies in S is a multiple of n" | n = 1,...,120} are true in every possible non-contradictory case?

Consider the set $S := \{$ "the number of lies in the set $S$ is a multiple of $n$" $|$ $n = 1, 2, 3, ... , 120 \}$. Question: Which elements/sentences in the set $S$ are true in every ...
630 views

### 125034 v1.0.0 / WR 1713-11-07

I am developing an app that generates puzzle games every day (https://125034.pages.dev/). Their basic form may be viewed as Wordle in math, Sudoku in 6 grids, or Einstein's Riddle in 1 row. If today ...
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This puzzle is part of the Puzzling Stack Exchange Advent Calendar 2022. The accepted answer to this question will be awarded a bounty worth 50 reputation.< Previous Door Next Door > Alice and ...
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### Unsure how to continue Sudoku solve/apply Y-Wing strategy

I am not new to solving a sudoku board, but I do not have a lot of experience with harder boards and more advanced strategies (I am able to solve a "hard" board in under 10 minutes, on ...
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