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).

Filter by
Sorted by
Tagged with
51
votes
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
95
votes
16answers
941k 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 ...
167
votes
22answers
75k 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 ...
40
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....
20
votes
2answers
10k 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 ...
16
votes
5answers
5k views

N logicians wearing hats of N colors

N logicians are wearing hats which can be of N different colors (each hat has one color; there can be multiple hats with the same color). Each logician can see the colors of all hats except his own. ...
43
votes
6answers
30k 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 ...
69
votes
26answers
15k 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,...
21
votes
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 ...
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 ...
18
votes
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 ...
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 ...
16
votes
5answers
2k views

Cards in the darkness

A man is sitting in a dark room. In front of him is a pile of 100 cards. He knows that there are 90 cards faced up and 10 cards faced down. Is it possible for the man to form two piles from these ...
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 ...
33
votes
3answers
5k views

Pirates and gold coins

A group of N pirates has come by a chest containing 200 gold coins. Their rules require that the coins be distributed by the following approach. The pirates are ranked from fiercest to meekest and ...
30
votes
7answers
5k views

Dinosaur egg drop

Archeologists discover two dinosaur eggs, and you are given the chance to test the durability of these eggs (bad move on their part). Suppose that these eggs will absorb a specific amount of force ...
14
votes
1answer
2k views

Knights and knaves in a foreign language

You die and ascend to heaven, there is a knight (truth-teller), a knave (pure liar) and a joker (random) sitting on a cloud - they all look the same. In order to gain entry you must determine their ...
13
votes
1answer
688 views

Heyacrazy: Crosses

This is a Heyacrazy puzzle. Heyacrazy is an original genre, inspired by the "two border" rule of Heyawake and Heyawacky. Rules of Heyacrazy: Shade some cells of the grid. Shaded cells cannot ...
5
votes
7answers
3k views

rescue operation - where is your partner?

Your partner's space ship has crashed on an uninhabited planet. Only the radio transmitter and his compass were still in operation. He asks you to rescue him, and tells you how to find him by the ...
50
votes
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. ...
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 ...
20
votes
3answers
6k 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)...
37
votes
3answers
6k views

The coolest checkerboard magic trick

In the small town of Terni (Italy), there's a couple of young friends named Marco and Leonardo, who like to perform magic tricks to a restricted audience of common friends and relatives. They like to ...
11
votes
3answers
816 views

Twelve Labours - Prologue

This puzzle serves to introduce the ‘Twelve Labours’ series of puzzles. Its solution is standalone and does not contribute to the meta-puzzle at the series end. “Wake up, wake up, wake up! What are ...
14
votes
1answer
6k views

Fastest way to cross a river: four people with different rowing speeds

This problem is commonly cited as a Microsoft interview problem, although I have paraphrased it here to involve a river and a boat instead of a bridge and a flashlight, and tweaked the crossing times ...
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 ...
14
votes
2answers
3k views

Product and Sum

My fellow mathematicians Paul and Sam are very fond of mathematical puzzles. One day, I came up with the idea on mathematical puzzles while three of us having lunch together. I: Hey, guys. I am ...
11
votes
6answers
10k views

1 Fake Coin among N Amount of coins

You are given $N$ coins which consists of only $1$ fake coin. You also have a sensitive old-fashioned Pan Balance Scale. You are asked to find the fake coin in totally 5 times weighing on the Pan ...
77
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.
21
votes
12answers
129k 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....
13
votes
1answer
3k views

The seven piece silver chain

You have to stay for 7 days in a hotel outside your city. But you forgot to bring your credit card and are out of cash. You have a silver chain with 7 links. The rule in this hotel is that residents ...
10
votes
5answers
1k views

Drawing a piece of paper, to be released or executed

There is a prisoner who will be executed, but there is a rule in the kingdom that says, "the prisoner will be given a bag containing a white paper and a black paper. If the prisoner is lucky enough to ...
8
votes
2answers
3k views

First day of school

Here's a pretty easy one. A new student (a male) was wandering down the hall of his new school looking for the boys' locker room. He asks a nearby student (who happens to be the school bully) to ...
34
votes
3answers
5k views

Do better than chance

You and an opponent are playing the following game: Your opponent picks two different real numbers, however he wants to, and writes them on two cards, which he presents to you face down You choose ...
27
votes
3answers
4k views

Differentiate between the numbers from 1 to 5 with one single yes/no question

This question requires a bit of logical distortion to get the information required to answer the question. However, I've never seen it asked before what would happen if more modes of question ...
15
votes
3answers
1.0m views

Brooklyn 99 riddle: Weighing Islanders [duplicate]

This one comes from this week's Brooklyn Nine-Nine episode! There is an island with 12 islanders. All of the islanders individually weigh exactly the same amount, except for one, who either weighs ...
56
votes
13answers
18k 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, ...
7
votes
4answers
387k views

Puzzle of putting numbers 1-9 in 3x3 Grid to add up to 15

In a 3x3 grid, I'd have to put numbers from 1 to 9 in a manner so that respective row, column and diagonal add up to 15. I have only been able to come up with one solution: $$\begin{array}{ccc} 6 &...
43
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 ...
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. ...
8
votes
4answers
2k views

The murder by the maid - Who is the murderer

A man was killed in a roundhouse with no doors or windows. Four maids were present at the time of the murder, but are saying nothing. When asked what they were doing they replied as thus: Maid 1: 'I ...
30
votes
2answers
2k views

Question 16 Ripple Effect

This is a Ripple Effect puzzle. The rules of this puzzle are: Fill in each region with numbers from 1 to n, where n is the region size. For instance, the top left region must have the numbers 1 to 5 ...
21
votes
2answers
449 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. ...
12
votes
4answers
6k views

Who is the thief? An elementary school teacher had her purse stolen

Its not mine. I found it and didnt find it when i searched so i hope you guys enjoy. I did edit it somewhat. An elementary school teacher had her purse stolen. The thief had to be Sammy, Karin, ...
9
votes
10answers
89k views

Deaf, Mute and Blind [closed]

There were three men. One was deaf, the other was blind and the third was mute. One day the deaf man kissed the blind man's wife. The mute man saw this and he wants to tell it to the blind man, but he ...
13
votes
7answers
2k views

Faulty computers

You have $99$ computers in a LAN room, and you know that at least $50$ are working. The others can be faulty. The only thing you are allowed to do is to ask computer $i$ the question "Is computer $j$ ...
10
votes
3answers
1k views

The Expedition Into The Ancient Cave

You are a archeologist and have taken 8 of your students on a expedition trip to a ancient cave to try and find ancient treasure. After you and your team entered the cave, you travel as a group ...
2
votes
2answers
3k views

The case of the 4 campers and the rickety bridge! [duplicate]

Four people need to cross a rickety rope bridge to get back to their camp at night. Unfortunately, they only have one flashlight and it only has enough battery left for seventeen minutes. The bridge ...
16
votes
1answer
599 views

Barrel - Part 1

An entry in Fortnightly Topic Challenge #35: Restricted Title 1. Title based on the very first xkcd. Continued in Barrel - Part 2, Barrel - Part 3, Barrel - Part 4, and Barrel - Part 5. You manage a ...
11
votes
1answer
823 views

The completely generalized poisoned-bottle problem

Since there have been quite a few poisoned-bottle problems posted to the site already, I thought I'd post a general formula to cover all future variations of this problem (at least where a single ...