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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163
votes
22answers
72k views

In the 100 blue eyes problem - why is the oracle necessary?

The riddle Randall Munroe (of xkcd fame) has, a bit hidden on his site, a logic puzzle: A group of people with assorted eye colors live on an island. They are all perfect logicians -- if a ...
130
votes
13answers
20k views

This is it. This is the one. Find your wife

If you have found her, maybe you could try saving her? You come home one day and find your wife is out. You open your computer and discover an email from her. To xxxxx, / Curiosity killed the ...
115
votes
7answers
41k views

Mensa IQ test question

Which of the 8 tiles below is missing? I've been trying to figure out the answer to this question for quite some time. Can anyone spot the pattern?
101
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15answers
37k views

My wife has died

In 1980, a man lives on the 30th floor of his building. Every morning he wakes up, gets ready, kisses his wife, takes the elevator down to the first floor, and goes to work. One morning, he wakes ...
91
votes
9answers
15k views

Five coloured doors, which leads to freedom?

You have been incarcerated in a high-security prison for several nefarious crimes which we need not go into here. The warden, being a kindly logician, offers you a single chance to escape. You are ...
91
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2answers
37k views

3 Logicians Walk Into a Bar

Three logicians walk into a bar. The barman says, 'Does everybody want a drink?' The first logician says, 'I don't know.' The second logician says, 'I don't know.' What does the third logician say? ...
89
votes
15answers
897k views

Two doors with two guards - one lies, one tells the truth

You are a prisoner in a room with 2 doors and 2 guards. One of the doors will guide you to freedom and behind the other is a hangman --you don't know which is which. One of the guards always tells ...
83
votes
7answers
15k views

Thanks, dad! Never again

No idea why my dad dragged me into this place. Some guy is performing on the stage. He's reading numbers out loud. I think it's some kind of a sequence puzzle. 1... 8... 9... 16... 17... ...
79
votes
18answers
14k views

Nine gangsters and a gold bar

One night nine gangsters stole a gold bar. When the time came for dividing the bar, they faced a problem: two of the criminals put guns to each other's faces. Now it's up to fate whether one of them ...
76
votes
11answers
21k views

Correct way to add 22 to 4 to get 82

Inspired by this other puzzle, tell me a correct way by which adding 22 to 4 will give 82. As in that other puzzle, these numbers are all expressed in base 10.
72
votes
9answers
12k views

Is a married person looking at an unmarried person?

I remember answering this one incorrectly and when the answer was explained to me I was annoyed with myself. Here is your chance, with the original word phrasing: Jack is looking at Anne, but Anne ...
70
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2answers
6k views

Oh dang, I have to change my whole answer!

One day, you enter your math classroom. On the board, there are the words POP QUIZ. Dang it! Was it about fractions? you knew you were bad with fractions. You look down. $\begin{array}{|cc|} \...
69
votes
13answers
15k views

Three logicians walk out of the bar

It is known that when logicians get drunk they may claim not to know the answer to a question when they should know it very well. After a night of heavy drinking at the bar, three logicians decide ...
68
votes
26answers
14k views

You have one question to tell whether the number I'm thinking of is 1, 2, or 3

This is an interesting puzzle which was passed to me by a friend some time ago. I do know the answer, but will refrain from self-answering on this to see where it goes. I'm thinking of a number: 1, 2,...
64
votes
8answers
258k views

Crack the lock code

Can any one know how to crack this? I got this as a challenge.
61
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4answers
4k views

Gerrymandering Puzzle - Rig the Election

The following graphic is a map of the country Mathlandia: You are currently running for reelection, but the polls aren't exactly in your favor. Each square in this grid is a county. Counties with a ...
60
votes
7answers
10k views

Three mathematicians are forever in Prison

I'm excited to share the following riddle. It was given to me more than two years ago and I finally solved it last summer (after not thinking about it for a long time). In my desperation, I tried to ...
56
votes
13answers
17k views

Are there eighteen or twenty bars in my castle?

Two friends, Mark and Rose, are very famous logicians; they are so clever that they can deduce any logic connection possible in a matter of minutes even from the most vague situation. Unfortunately, ...
56
votes
3answers
6k views

Left coin, right coin, last coin?

In this game, all players start sitting at a round table, each with a coin in their hand. At every turn, all players toss their coins together and put them on the table in front of them. Then each ...
56
votes
2answers
8k views

It's getting harder and harder not to offend anyone

Andy, Bob and Chuck are old friends meeting for the first time in years. Scene 1: At the intersection ANDY: Hey guys! Long time no see! BOB: Hey, nice to see you, Andy! Have you seen Chuck? Is ...
55
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5answers
4k views

Who shall come to the tea party?

All of your stuffed animals are assembled, anxiously waiting to learn who will be be invited as the Guest of Honor to your next tea party. This is to be an exclusive party, after all, as there is ...
53
votes
10answers
8k views

A well balanced puzzle: Logic puzzle(s) in visual disguise

This is a rather involved puzzle and might require a bit of stamina. All of the puzzle is in image form. The introduction text is not needed for the puzzle. At the end of the puzzle you'll get a short ...
52
votes
4answers
5k views

Is this chromatic puzzle always solvable?

I've created a new puzzle from an Alexey Nigin's idea. It consists of a 8x8 board where each square is randomly assigned one of three colors. A movement is defined by picking any two orthogonal ...
51
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17answers
10k views

How can I convince my colour blind friend that his two balls have different colours? [closed]

This question is inspired by this one, inspired by another StackExchange network question. My colour blind friend has two balls, one red and one green. However, he is convinced that they are the same....
50
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3answers
5k views

Sliding Bolt Puzzle

You are in a room with two adjacent doors locked by four sliding bolts. The bolts are movable and block only one door at a time; however, you do not know which bolt currently is blocking which door. ...
49
votes
11answers
9k views

Turning a goat?

This is a goat made up of 5 sticks. You have to move (change position) any one stick of them such that its head turns to the right side (above the right leg). Notice currently its head is on the left ...
49
votes
8answers
15k views

The Cucumber Paradox

Suppose you have 100 lbs of cucumbers and these cucumbers consist of 99% water. You decide to leave the cucumbers in the sun for a while until they consist of 98% water. You bring the cucumbers back ...
49
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4answers
8k views

Interview Question or Pathbreaking puzzle

I thought this changes the way series of numbers are looked at 1 1 1 2 1 1 2 1 1 Write down the next three lines
49
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2answers
4k views

A Robot's Last Words

There, spread out all over the floor, were the mechanical pieces of a robot. Something had torn it apart, and the debris spanned a radius of a few meters. There was no sign of what might have caused ...
48
votes
9answers
16k views

One hard IQ question

Can someone explain me the logic behind this? The question is: What comes next in the pattern (out of the 5 possibilities)
48
votes
15answers
6k views

Find the identity of the four troll brothers

The four troll brothers Wudhor, Xhaqan, Yijlob and Zrowag have the following properties: Wudhor always says the truth. Xhaqan always lies. Yijlob lies or says the truth unpredictably. ...
47
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4answers
5k views

Batman and the piano

Batman: Alfred. Are you there? Alfred: Yes, Master Bruce. How may I help you? Batman: ...
46
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10answers
15k views

Puzzle: Who hacked the computer?

I was working my way through some Knight and Knave Puzzles in Discrete Maths by Rosen, when I came across the following question: Four friends have been identified as suspects for an unauthorized ...
45
votes
1answer
2k views

Edward's Maze I

Edward's "revenge" on Bob the mute house servant Edward had enough! This was it! During the yearly sorcerer meet in a hidden cellar in Léon, Edward discovered a red stain on his precious robe. ...
44
votes
8answers
9k views

Haters gonna hate

In a classroom, there are $20$ students and every student mutually hates exactly $3$ other students in the class. (If X hates Y, Y hates X as well.) The principal summons some of the students from ...
44
votes
3answers
2k views

Tiling with T-tetrominos in gravity

The goal is to tile all the white squares using T-tetrominos when there is gravity pulling the tetrominos downwards like regular tetris. The black squares are void and the ground is just below the ...
44
votes
2answers
3k views

Reverse Puzzling

George is a great puzzler, so I was extremely surprised when he didn't immediately know the answer to a really famous puzzle. It's a puzzle that you probably did years ago, and have heard so often ...
44
votes
3answers
11k views

I don't know the two numbers… but now I do

Two perfect logicians, Summer and Proctor, are told that integers $x$ and $y$ have been chosen such that $1 < x < y$ and $x+y < 100$. Summer is given the value $x+y$ and Proctor is given the ...
44
votes
10answers
4k views

Clever Jack - A logical fairy tale

As so often happens in fairy tales, there once was a king who had an intractable problem, one that even his wisest advisers could not solve. After many years of frustration, the exasperated king ...
43
votes
6answers
29k views

Hats and Aliens

Here's a neat little puzzle taken from a Google interview question: 10 humans are abducted by aliens; each represents 10% of the entire human population. The aliens give each abductee either a ...
42
votes
11answers
8k views

3 doors, three guards, one stone

You are in a room with three doors. You find out that behind two of these doors, the darkest pit of hell is waiting for you to make a mistake. The other door leads to heaven, where you obviously want ...
42
votes
2answers
5k views

A crossword so simple, it practically solves itself

An entry in the 19th fortnightly challenge... A Grid Some Clues There are three examples of this in the finished grid Two answers that touch a corner, in relation to 25A (D) Contained in the ...
42
votes
1answer
2k views

The Persistence Of Memory

You find yourself on the floor, slowly waking up and unable to remember how you got here. As you slowly come to your senses, you realize that another weird guy has trapped you in another unfamiliar ...
41
votes
8answers
30k views

How did the police know?

One night, a man receives a call from the police. The police tell the man that his wife was robbed, murdered, and her body dumped in a remote location, and that he should reach the crime scene as soon ...
40
votes
7answers
5k views

Amnesiac in a ring shaped palace

Related: Turn off all lights in a ring-shaped palace Your boss has trapped you inside a ring-shaped palace, and all you know about the palace is that there are some number* of identical rooms, each ...
39
votes
5answers
6k views

Burning ropes as timers

You have 2 identical ropes which burn at a specific rate, and an unlimited supply of matches. When you light one end of a rope, the fire will take exactly 1 hour to travel to the other end of the rope....
38
votes
3answers
11k views

How many liars are in the room?

There are five people in a room. Each person is either a knight, who always tells the truth, or a liar, who always lies. Each person is asked the following question: How many liars are among you?...
38
votes
3answers
7k views

Hungry lions and a goat

There are 53 lions in a cage and 1 goat. All the lions are very hungry and would want to eat the goat. But the problem here is that any lion who eats the goat can satisfy his hunger but he will ...
38
votes
1answer
4k views

So how did the date go?

It's Monday morning. Fernando just sat down at his desk for another hard day at work - programming stuff and answering telephone calls - "have you tried turning it off and on again?" As he is about ...
38
votes
9answers
5k views

An old picture puzzle

Here is a drawing of an old picture. Your task is to answer all 8 questions correctly AND give a good reasoning for it What time of day is it? Is it early spring or a late fall(autumn)? Is this river ...