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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20
votes
5answers
7k views

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). ...
20
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8answers
10k views

Logic puzzle - 3 suspects

An inspector knows that exactly one of 3 suspects committed a crime, and interviews them to find out which. Each person lies one time, and tells the truth the other time. A says: I did not do it. B ...
20
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3answers
5k views

Too Many Damn Buffalos [closed]

"Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo" The sentence above is an actual sentence which makes perfect sense and is not wrong. The word "Buffalo" has three meanings: ...
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5answers
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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: ...
20
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3answers
5k views

The lake monster

You are on a rowboat in the middle of a large, perfectly circular lake. On the perimeter of the lake is a monster who wants to eat you, but fortunately, he can't swim. He can run (along the perimeter)...
20
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5answers
2k views

Knights and knaves in Landilandia

You're traveling on a hiking trip in the land of Landilandia when you encounter a forest. The notes in your guidebook tell you that there's a safe route here leading into the woods, but when you ...
20
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12answers
122k 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....
20
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3answers
1k views

The mysterious card in the middle

The referee tells Lefty, Righty, and Middly: "I have picked three positive integers $L,M,R$ with $L<M<R$ and $L+M+R=13$, and I have written these numbers onto the three cards lying face down on ...
20
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7answers
3k views

Ali Baba and the 10 thieves

EDIT: This puzzle originates from the "International Mathematics Tournament of the Towns", and was published in the book "S.M.A.R.T circle overview" by Professor Andy Liu. The author has (albeit a ...
20
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2answers
9k 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 ...
20
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2answers
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 ...
20
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3answers
3k views

Sum of secret numbers is 101

Alice, Bob, and Charlie were given three numbers, respectively. They were said that all the three numbers were positive integers and the sum was 101. Alice: I know we have different numbers. Bob: ...
20
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1answer
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 ...
20
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1answer
2k views

The Illuminati and the Knights Templar

Some people in the American Senate are working for secret organizations. Some work for the Illuminati, some work for the Knights Templar, and some work for both. The are also innocent citizens who are ...
20
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1answer
2k 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 of ...
20
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4answers
3k views

A Knight or a Knave stood at a fork in the road

A competent logician was traveling home down an unfamiliar road. As he approached a fork heading in two different directions, he noticed a lone figure standing directly between the two routes. The ...
20
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1answer
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 ...
20
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4answers
9k views

Determine the number $r$ from the statements

Alice and Bob are perfectly logical and super intellegent. Their professor decides to play a game with them, and he tells them: "I have chosen two numbers (integers) $x$ and $y$ with $2\le y \le x\...
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4answers
1k views

The Prison Escape Pt. 1 (THE DOOR)

You are currently escaping a prison owned by a mad scientist. As you were about to approach a large iron door that you think should be leading to the exit, a guard came out from the shadows. ...
19
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4answers
6k views

Who stole the flying car in Hogwarts?

During a trial in a Hogwarts court, Ron claimed that the Flying Ford Anglia car was stolen by Hermione. Then Hermione and Harry gave testimonies which, for some reason, were not recorded. Later on ...
19
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5answers
1k 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 ...
19
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3answers
3k views

The origin of the blue eyes puzzle

The Blue Eyes puzzle is possibly the most popular induction-based puzzle known. Is it really known who was the first to come up with it (in any form). The link at xkcd says: I didn't come up with ...
19
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6answers
3k views

Trapped in my Cellar

I have taken Doorknob hostage in my cellar. He is "perfectly" trapped - solid walls, solid floor, solid roof, no windows, etc. The only way out is a steel door and the only way to unlock the door is ...
19
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3answers
2k views

Which two houses didn't get any mail that week?

Postman delivers the mail in the small village. This village has exactly ten houses, numbered from 1 to 10. In a certain week, he did not deliver any mail at two houses in the village but at ...
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3answers
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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4answers
2k views

Escape The Strange, Code-Filled Cave

You awake in a weird cave with something strange written on the wall. You find a small piece of paper on a rock. It says the following: Solving each code and entering it into the password entering ...
19
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2answers
1k views

Miss Toad and her frogs

Miss Toad owns a lot of frogs. These frogs are all looking the same, but they can be either mad or nicely. If a mad frog is in a room with 3 nicely frogs, then he turns red, because he is ashamed. ...
19
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2answers
564 views

Deer-hunting in Mesak

The following are ten sentences in the Mesak language: ...
19
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5answers
2k views

Find the 8-digit number

A secret number has each one of its 8 digits colored either blue or red. Here are some clues: 1. All digits from 1 to 8 appear in the number. 2. The first two digits are not consecutive. 3. The ...
19
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2answers
2k views

Chess, for short people

Your grandfather and grandmother are playing chess, and you are sitting in the same room doing your own thing. A wide grin comes across your grandfather's face, and you can tell he is about to ...
19
votes
1answer
501 views

The Drouble with Doorples

You are the first officer aboard the Starship Enterpuzz, and moments after your captain departs for his week-long vacation, you discover that your ship is infested with tiny creatures called doorples. ...
19
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1answer
680 views

Numbered Logicians near the Blue Eyes island

There is an island near the famous Blue Eyes island where 100 perfect logicians live, each with a number between 1 and 100 (repetitions allowed) tattooed on their forehead. They know all the numbers ...
19
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1answer
5k views

Can you solve this logic puzzle in disguise? The color code behind the tomb

Another themed puzzle for you to enjoy. As with all my puzzles, please provided feedback about pro's and cons of the puzzle. The puzzle is self-contained (the link is just to provide a theme) and I ...
19
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1answer
1k 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 ...
19
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2answers
2k views

How to create a pure mathematical-logical based puzzle equivalent to resistance based physical puzzle?

I am thinking how to reformulate a physical puzzle in a way that it becomes purely logic based (doesn't uses physical lows and can be solved by a person, who knows nothing about physics). The puzzle: ...
18
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9answers
1k views

One-one communication

5 people are standing in a circle - person A needs to tell his salary to person B, but none of the others should know A's salary. How is this possible, if every person only whispers to the person on ...
18
votes
6answers
3k views

Guess five binary digits!

Person A thinks of a 5 digit binary number. Person B tries to guess the number. B can guess a 5 digit binary number and A will respond with the number of correct digits (digits in the right place). ...
18
votes
2answers
57k views

A man with two red pills and two white pills

Story: A Color blind man is travelling in a somewhat famous ship that had just a few people on board. Everything was smooth sailing for some days. One day,the man heard some noises from outside when ...
18
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7answers
3k views

House Number Mastermind

I was having a party at my new 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. I was ...
18
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2answers
2k views

We are two immediate neighbors who forged our own powers to form concatenated relationship. Who are we?

Our concatenated number is $ \overline{ABAC}, $ where $ A, B, C $ are all positive digits (1 - 9). Our relationship is $$ \overline{ABAC} = A^A + B^B + A^A + C^C $$ Who are we?
18
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8answers
3k views

What Imprisonment sentence will immortal citizen soldier Guilt receive?

On planet Immortal, everyone lives forever but essential resources (including food and supplies) on the planet are limited. Ultimatopian raiding swords are the most effective weapon available to loot ...
18
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6answers
2k views

Can YOU guess this Riley Riddle?

My Prefix returns us to the dark ages. My Infix belongs to someone. My Suffix has annoyed me since birth. Hint 1: Hint 2:
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8answers
2k views

When should you rest?

You are in an airport and are worried about missing your flight. So you start to run the long distance to the flight gate at a steady speed of 10km/h (you have bags and are not very fit). ...
18
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5answers
3k views

Statements that the deities True and False cannot say

You over exert yourself working on logic puzzles and die of exhaustion. You are awoken by the omniscient deities True and False. True only speaks true statements and False only speaks false statements....
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2answers
1k views

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. ...
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2answers
2k views

Fairy Chess #1- The Mastermind

(Fairy chess is a general term for any kind of chess variant with pieces that aren't used in the normal game) (Inspired by The Black Prowler (chess)) In this variant, white has their entire army ...
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3answers
3k views

Knights and jokers

There are $N$ men. $K$ of them are knights, $M$ of them are jokers. $N$ is known, $K$ and $M$ are unknown. You know that: $K + M = N$, $K \gt M$, $M \ge 1$, $N$ is odd. Knights always tell ...
18
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8answers
2k views

30 fake coins out of 99 coins

You are given 99 coins which consists of 30 fake ones. You also have a digital balance scale with perfect precision that shows how much difference between weighs you put on. For example, if you put 10 ...
18
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2answers
831 views

Find the safe path through the dungeon!

You need to get from the bottom to the top. But this dungeon puzzle is extremely ancient, and unfortunately, the symbols on the tiles are no longer visible. Stepping on an unsafe tile means certain ...
18
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2answers
2k views

Someone has vandalised this long division. Can you reconstruct it?

Oh dear, someone has vandalised this long division. They've replaced every digit either with a wrong digit or a hyphen. Your task: reconstruct the entire thing. There's no remainder. Please show ...