# 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 Minesweeper Sudoku

My brother created this puzzle, and he wanted me to post this here. Each 3x3 box contains three mines (those squares also have numbers in them). There are no mines in boxes containing a 1, 2, or 3. ...
1k views

### The Blank Sudoku

An entry in Fortnightly Topic Challenge #47: "Wacky Sudokus" (h/t to Beastly Gerbil, whose 1,2,3... Trinary!!! puzzle provided inspiration for this puzzle) This puzzle is a normal Sudoku, ...
2k views

### What is the solution to Lewis Carroll's “Froggy's Problem”, and what is the “trap”?

Froggy's Problem was presented in Lewis Carroll's Symbolic Logic, with a note that it "contains a marvellous trap". Because Carroll never released Part 2 of Symbolic Logic, its solution is unknown. ...
23k views

### Which day of the week is today?

7 people are arguing what the current day of the week might be. Each states what he believes to know: The day after tomorrow is Wednesday. No, Wednesday is today. You are both wrong, Wednesday is ...
2k views

### This new puzzle type needs a name {6}

I believe I have invented** a new type of puzzle... What is its name? Begin by solving the Fillomino puzzle: Rules of Fillomino (adapted from Nikoli) Fill in all empty cells with numbers under the ...
7k views

### Variation of 100 prisoners light problem

There is a classic problem below for which Dr. Yisong Song wrote a very well written and thought out series of solutions. The variation here I've never seen anywhere but am curious. I want to work it ...
2k views

### They are all names of Movies ; aren't they?

Here is a simple list of some of my favorite movies. Please fill out the blank. I will even give you 4 choices! 1 The Sting 2 In the Heat of the Night 3 ? 4 Unforgiven 5 Braveheart 6 The Aviator The ...
4k views

### Logic puzzle: Driving around the United States

For Super Bowl Sunday, here's a super-sized logic puzzle! This was a practice puzzle for a hunt I participated in a few years ago. There are ten delivery drivers driving around the United States of ...
17k views

### Get 100 as an answer on a calculator without using 0

Task Get 100 as an answer with only four keystrokes on a regular calculator. Disallowed keys 0 00 Allowed keys All other than the aforementioned two keys. Take the below image as a reference. ...
4k views

### Knights and Knaves : Liar , Liar - How many are you?

There are 2014 persons in a row Each of them is either a Knave (who always lies) or a Knight (who always tells the truth). Each person says 'There are more knaves to my left than knights to my ...
3k views

### On which day The Joker usually going on a date?

You are an investigator. You are to investigate The Joker to know on which day he usually goes on a date with Harley Quinn. The Inspector said that The Joker is lying if and only if it's Monday, ...
12k views

### Coin weighing problem

You are given ten stacks of golden coins, each stack consisting of ten coins and a digital scale with arbitrary precision. You know that all stacks of coins are made from gold, weighing 10 grams per ...
2k views

### Can the assistants open the safes?

I'm working as a file manager. My company bought me three safes and assigned me three assistants. I'm busy most of the time and I can't manage the safes myself, so I need to let my assistants access ...
1k views

### New logical puzzle

The goal is to divide the grid into regions of exactly four cells (tetromino). Each region contains exactly two different symbols. Regions of the same shape must contain the same symbols. The ...
3k views

### 3 Numbers on Hats, A = B + C

This feels like it should be a common puzzle, but I haven't found anything exactly like it searching online, so here goes. Apologies if it's a duplicate. Three logicians, person 1, 2, and 3, along ...
3k views

### Winning an unfair game

I came across the following interesting problem today: A game consists of a sequence of plays; on each play either you or your opponent scores a point, you with probability 𝑝 < 1/2, he with ...
2k views

### This puzzle design was a DISASTER!

As any member of the PSE community knows, grid-deduction puzzles really aren't my forte. In fact, I'd like to share one particularly disasterous attempt at designing a Slitherlink puzzle. Disclaimer:...
2k views

### Art Accident at Airport!

There was an accident at the airport! A hanging art installation fell and landed on some passengers. In addition to tearing up all their tickets and mixing up their luggage, six people sustained ...
2k views

### The last question to the guards

"What will happen next?" asked the old man. His voice was friendly, his eyes bright, as always. His hair and beard seemed to be even whiter than ever before. "The standard procedure is as follows: ...
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### Introducing: Compoundoku!

Rules of Compoundoku: Solve both left and right Sudokus. In addition, the board below them is the Compound Board of both Sudokus. Each number on the Compound Board should tell either: (1) ...
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### Can you put L trominos to fill the figure?

In the above picture, there are 24 squares. Can you only use L trominos to fill the figure? If yes, give an example. Otherwise, please explain why. An L tromino is like this:
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### Which box is safe to open?

One day, you enter your house...and find it has been burglarized. On the table, a note says, "Thank you for your valuables. In return, I left a gift in the basement." Quite confused, you ...
3k views

### House Number Mastermind

I was having a house-leaving party at my old house, and challenged four of my friends to guess the number of the new address, which had three digits. The responses I got were 280, 376, 304, and 370....
4k views

### The Dwarves' Test

One day, the chief of the dwarves decided he wanted to test his tribe. So that night, he told the dwarves that he would paint on each dwarf's back a dot colored either red or blue. Each dwarf will ...
3k views

### The Monty Hall problem

I'm amazed that, although well known, this problem hasn't been posted yet. Monty Hall You are on a game show. The host of the show shows you three doors. He tells you that behind one of them, is a ...
3k views

### Connect the Pipes

Each pipe shown on the left (A through I) connects to exactly one pipe on the right. To hide the answer, I have put a curtain over the pipe crossings and grayed out the pipe colors on the right side. ...
178k views

### Four prisoners wearing black and white hats

There are four prisoners. All four prisoners will be freed, if at least one of them correctly guesses the color of the hat on his head. They can't speak to each other, and they can't touch each other....
3k views

### My wall clock is not working

When I came back from my vacation I saw my wall clock has fallen down and not working. The clock was on the floor and all its numbers were detached from their positions. Can you help me to find out at ...
1k views

### Edward and the seven imps' Game

Excerpt of “Manipulating the Fabric of Space” “Miscasting translocation spells can have many nasty consequences. The caster’s body could be warped or torn apart, his soul could be separated ...
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### Heyawake: An Introductory Puzzle

This is a Heyawake ("divided rooms") puzzle. Rules of Heyawake: Shade some cells of the grid. Shaded cells cannot be orthogonally adjacent; unshaded cells must be orthogonally connected. ...
6k views

### The village of the liars and truth-tellers

I read this puzzle in an Italian newspaper some days ago. It reported it was asked at one of the latest Mathematical Olympiads. It's not difficult, but it requires some logical thinking. I'm posting ...
3k views

### How do I tell the children's ages?

My friend once told me a logic puzzle along the lines of: A student asks a teacher what the ages of the teacher's three kids are. The teacher said, "the product of their ages is 72, and the sum ...
582 views

### Statue View: Tetrominoes

This is a Statue View puzzle, an original invention combining two logic puzzle genres: Statue Park and Canal View. Rules of Statue View: Shade some cells of the grid to form the given set of pieces. ...
792 views

### The answers to these questions are?

C is the correct answer to how many questions? A. 1 B. 2 C. 3 D. 4 Which letter is the correct answer fewer times than any other? A. D B. B C. C D. A Which letter is the ...
558 views

Rules of Slitherlink: Connect adjacent dots with vertical or horizontal lines to make a single loop. The numbers indicate how many lines surround it, while empty cells may be surrounded by any number ...
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### Which is worth more - a chest of nickels or half a chest of dimes?

I have two large identical chests of exactly the same shape, volume, etc. One is completely full of nickels (each worth 5 cents), and the other is exactly half full of dimes (each worth 10 cents). ...
5k views

### The Knight never lies, the knave always lies, and the spy either lies or tells the truth

A says he is not the knight, B says he is not a spy, and C says he is not the knave. Who is who?
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### Can you open the door or die? v2

This is the follow up question to my previous question You wake up and find yourself in a very strange room with a single door. You find a note on the ground surrounded by lots of cards: ...
3k views

### Robots in a spaceship [duplicate]

Xerxes has 6, 7 and 8-arm robots in his spaceship. Unfortunately, the 7-arm robots are misprogrammed and everything they say is a lie. The other robots are fine, they always speak the truth. Once ...
2k views

### Single Colour Mastermind Problem

Imagine we're playing a game of mastermind with the usual eight colours, only this version has six holes across in which to place colours. And to make it easier for you I tell you that I have filled ...
2k views

### What's in my pocket? [duplicate]

Well, I can tell you Johnny has memory cards in his pocket. Back Story My brother, Johnny, is a tech nerd. He loves gadgets of all kinds. As a matter of fact, you can be sure at any one given time, he ...
13k views

### Which one is the true statement? [closed]

All five statements below are true. None of the four statements below are true. Both of the statements above are true. Exactly one of the three statements above is true. None of the four statements ...
3k views

### Ten Tricky Mathematicians

Somewhere on the Hyperbolic Plane, you encounter ten mathematicians. You know that some of them always tell the truth while the rest always lie. Each of them knows which of the others tell the truth ...
2k views

### Emeralds bet - A round world

It was the 15 October 1502, just a few hours before midnight in an old tavern at the docks. Emerald raised two fingers, after repeatedly looking at his three cards, before finally answering the ...
2k views

### What will the Frenchman say?

An Englishman, a Frenchman and a German are speaking. First the Englishman says : "M". Then the Frenchman says : "M" as well. And the German also says : "M". They all agree and decide to ...
1k views

### Masyu jigsaw puzzle

Here's a masyu puzzle for you. The rules are as follows Draw a single closed loop which does not cross or touch itself. The sections of the loop run horizontally or vertically between the ...
1k views

### Chess Connect Puzzle

I made up a new logic puzzle based on the games Numberlink and Chess, and thought it ended up rather interesting. The solution, as usual, is unique. The starting and ending positions of 7 chess ...
1k views

### Statue Park: Knight's Lines

This is a Statue Park puzzle. Rules of Statue Park: Shade some cells of the grid to form the given set of pieces. Pieces may be rotated or reflected. Pieces cannot be orthogonally adjacent (though ...