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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23
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2answers
1k views

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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3answers
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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2answers
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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 ...
22
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4answers
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 ...
22
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9answers
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....
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5answers
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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 ...
22
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12answers
151k 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....
22
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3answers
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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 ...
22
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2answers
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 ...
22
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3answers
2k 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 ...
22
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1answer
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 ...
22
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4answers
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 ...
22
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2answers
771 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 ...
21
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5answers
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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). ...
21
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6answers
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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3answers
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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:
21
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8answers
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Robots in a spaceship

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 ...
21
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9answers
4k views

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 ...
21
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8answers
12k 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 ...
21
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3answers
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 ...
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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 ...
21
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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 ...
21
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3answers
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 $p < \frac{1}{2}$, he ...
21
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2answers
502 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. ...
21
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1answer
1k views

My Grandfather's Final Message

As my grandfather reached the end of his long and satisfying life, I sat by his bedside and asked him what advice he could give me to help me in my own. Unable to speak, he pointed to his bedside ...
21
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1answer
3k 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 ...
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8answers
11k 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: ...
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5answers
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 ...
20
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2answers
58k 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 ...
20
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4answers
2k views

What's in my pocket?

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 ...
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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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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 ...
20
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3answers
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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 ...
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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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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: ...
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3answers
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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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1answer
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Isometric Heyacrazy - Now In 3D!

This is a Heyacrazy puzzle on an isometric grid. Rules of Heyacrazy: Shade some cells of the grid. Shaded cells cannot be orthogonally adjacent; unshaded cells must be orthogonally connected. When ...
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 ...
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4answers
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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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1answer
845 views

Unbalanced weight of boxes

You are given a traditional balance scale with two pans (no reading) and 6 boxes with the following properties: 1) the weight of each box is a positive integer number 2) if you put any number of boxes ...
20
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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 ...
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\...
20
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1answer
554 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. ...
20
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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
7k 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 ...
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4answers
3k views

After here should I guess or is there a logic solution on Sudoku?

From this point is it necessary to guess or is it possible to find a logic solution?
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3answers
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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 ...

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