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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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27
votes
4answers
7k views

How do I arrange pencils so they all touch each other?

How do you arrange 6 pencils so that each one touches the other five? And what about 7 or 8?
27
votes
5answers
4k views

First odd number in a “number dictionary”

All numbers between 1 and 1010 are written out and ordered alphabetically into a dictionary (as the only entries). Spaces and hyphens are removed. 1024 would then be "onethousandtwentyfour". Also, "...
27
votes
13answers
12k views

Protagoras's Paradox. An Unsolved Court Case

Many years ago, a Law teacher came across a student who was willing to learn but was unable to pay the fees.The student struck a deal saying, "I will pay your fee the day I win my first case in the ...
27
votes
12answers
2k views

Shapes and letters. What is the missing box?

Finally, someone has figured it out. Good job.
27
votes
13answers
5k views

Five hats and four logicians in a circle

I found this question in a book. The solution is correct (and complicated). No tricks involved. Four men were seated around a table. They were blindfolded and a colored hat was placed on each of ...
27
votes
5answers
1k views

Council of Magic - a palace of deceptive spellcasters

Council of Magic: The King of Puzzlington has sent you to a distant palace to gain the aid of the Council of Magic. As your luck would have it though, spellcasters are a tricky sort. There are 4 ...
26
votes
6answers
5k views

A Special Parking Lot

There is a special kind of parking lot that stores special 1x1 cars that only can move to adjacent squares not including diagonals if they are empty (provided no car occupies the square). Every car ...
26
votes
5answers
5k views

A simple visual puzzle to die for

Can you figure out how the patterns in the picture were generated, and determine what the hidden pattern at the bottom right should look like? This is a visual puzzle, and the solution can be ...
26
votes
5answers
5k views

You trolls, get out of my party!

You have invited $2017$ of your acquaintances to a party. But after they all arrive, you come to know from a reliable source that each of your guests is either a troll or a true friend. You don't know ...
26
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4answers
1k views

Reverse Puzzling 4

[This continues prior Reverse Puzzling here, here and here] George rubbed his hands together with glee. "So this is Andrea's puzzle, is it?" "Yes," I answered. "It's the first of them, anyway." "...
26
votes
4answers
6k views

Double whammy murder case! What happened?

It's Friday the 13th, and you and a group of 7 friends from the "Survivor" club belonging to University LeMao (A, B, C, D, E, F, and G) go camping. You're all pretty good friends, and talk quite a ...
26
votes
2answers
2k views

The Prognosticator

As I traveled across the web, searching far and wide, I came across an odd puzzle that made me feel awry. It foretold the future's path and predicted no tie. How could this puzzle work, and what was ...
26
votes
1answer
3k views

The tough one from “A Brilliant Young Mind” (2014)

Great movie by the way. I'm quoting from memory, so I may get the wording wrong. The positive integers are each colored Red, Yellow or Green. Prove that for any such coloring, there must exist ...
25
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13answers
5k views

3 Planks, 1 nail [closed]

John and Bob were doing some home construction and decided to take a beer break. Before grabbing a seat John pulls out 3 planks of wood, 1 nail and a hammer. John makes a bet with Bob saying I'll ...
25
votes
11answers
7k views

What is my four digit car number?

My car has a four digit number. Its last digit is double the first digit its middle two digits are the same its last two digits are double the first two digits What is my car's number? ...
25
votes
11answers
6k views

Kill the jokers! - Part 1

The famous and ruthless explorer Wyoming Wilbert reports in one of his books that he once visited an island inhabited by jokers and truth tellers. Truth tellers always tell the truth, whereas jokers ...
25
votes
10answers
4k views

Liar and the Truth teller with 6 inhabitants

There are two types of people on an island: truth tellers and liars. Truth tellers always tell the truth, while liars always lie. A foreigner meets six of the inhabitants, and asks each of them the ...
25
votes
3answers
2k views

A game of multiplication and addition

Carol is playing a game with Alice and Bob. She secretly chooses two integers between 1 and 10 and gives the sum to Alice and the product to Bob. After some time, the following discussion occurs: ...
25
votes
4answers
8k views

King Octopus and Servants Puzzle

Puzzle: King Octopus has servants with six, seven, or eight legs. The servants with seven legs always lie, but the servants with either six or eight legs always say the truth. One day, 4 servants ...
25
votes
5answers
3k views

How much red sand and how much blue sand?

This is a puzzle I remember arguing with my sister about when we were little... (Not quite as loud (or as public!) as the Monty Hall argument we had.) You have two large beakers of the same size. ...
25
votes
4answers
8k views

How do you solve a word puzzle when you have no idea where to start?

When you're looking at a logical word puzzle, what sorts of clues should you try to look for to solve them? There have been quite a few puzzles posted to this site so far that I spent a few minutes ...
25
votes
2answers
851 views

Bongard n°1: Fruit Flies

I increased the size of each space but the rules are the exact same as in the original problems published by Bongard. I'm adding a link in case people aren't familiar with this type of riddles Click ...
25
votes
1answer
2k views

Four is Cosmic!

This is a little puzzle I heard a while back from one of my mathematically inclined friends- I get the sense that it's bounced around a little, so forgive me if you've heard it. There is a sort of ...
25
votes
1answer
2k views

Create a Word Search

Create a word search with the following conditions: Use the eleven words below. They can be spelled up, down, left, right, or any of the 4 diagonal directions. ZERO ONE TWO THREE FOUR ...
24
votes
5answers
4k views

The No-Straight Maze

Consider the following maze. You can walk on the black lines, and your aim is to go from the green at the maze's bottom to the red on the left side. However, each time you reach an intersection of ...
24
votes
10answers
3k views

Thirteen politicians

Yesterday evening there was a public discussion on TV that was dedicated to the upcoming elections. Thirteen politicians from the thirteen most important political parties participated in it. After ...
24
votes
3answers
2k views

What is the missing number in this sequence?

1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-?-1-1-1 What is the missing number in this sequence? Note: The answer is not $1$.
24
votes
3answers
2k views

A Space Station 13 tricky situation

You are the Captain of the Space Station 13, and everything went bad very quickly. Most of the crew died, and it took you not so long to figure out that some people are not who they're supposed to be (...
24
votes
1answer
1k 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. ...
23
votes
5answers
6k views

Is there a proof that a map of the United States requires 4 colors?

The Four color theorem states that no more than four colors are required for any map. Can it be proved or disproved that 3 colors can be used for United States map?
23
votes
5answers
10k 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 ...
23
votes
6answers
16k 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. ...
23
votes
2answers
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 ...
23
votes
4answers
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 ...
22
votes
2answers
3k 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 ...
22
votes
4answers
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. ...
22
votes
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
votes
2answers
5k 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
votes
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
votes
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
votes
2answers
749 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 ...
22
votes
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: ...
21
votes
6answers
4k 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?
21
votes
8answers
3k views

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
votes
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 head down to ...
21
votes
5answers
3k 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 ...
21
votes
12answers
128k 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....
21
votes
8answers
10k 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
votes
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 ...
21
votes
3answers
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 ...