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).
573
questions
59
votes
4
answers
10k
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
- 4,992
129
votes
16
answers
1.6m
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, but the guards do know.
One of the ...
- 5,718
195
votes
26
answers
95k
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 ...
- 2,270
44
votes
6
answers
8k
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....
- 3,383
23
votes
2
answers
12k
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 ...
- 2,446
23
votes
5
answers
7k
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. ...
44
votes
6
answers
34k
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 purple ...
- 2,178
16
votes
3
answers
2k
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 ...
- 134k
14
votes
1
answer
834
views
The Blind Killer - a new series! SS#1
An entry in Fortnightly Topic Challenge #47: "Wacky Sudokus"
Other puzzles in this series
Welcome to a new sudoku series! This series will run for the duration of the current Fortnightly ...
- 56.4k
76
votes
28
answers
19k
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,...
user20
22
votes
1
answer
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 ...
user20
53
votes
3
answers
7k
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.
...
- 968
39
votes
3
answers
6k
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 ...
- 7,671
25
votes
1
answer
3k
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 ...
- 1,790
24
votes
4
answers
4k
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 ...
- 719
18
votes
3
answers
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 the truth, ...
- 16.1k
48
votes
4
answers
16k
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 ...
- 2,344
16
votes
5
answers
3k
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 ...
- 648
14
votes
1
answer
1k
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 ...
- 145k
7
votes
7
answers
4k
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 ...
- 731
23
votes
1
answer
1k
views
Statue Park: Knight's Lines
This is a Statue Park puzzle.
Rules of Statue Park:
Shade some cells of the grid to form the given set of pieces. Pieces may be rotated or reflected.
Pieces cannot be orthogonally adjacent (though ...
- 145k
15
votes
2
answers
3k
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 ...
- 12.8k
28
votes
3
answers
9k
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)...
- 2,106
26
votes
4
answers
9k
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 ...
- 2,393
17
votes
1
answer
870
views
Tapa - Confluence
This is a Tapa puzzle.
Rules of Tapa:
Shade some cells of the grid. Shaded cells should form a single [orthogonally] connected group; no 2×2 square should be fully shaded.
Some cells have ...
- 145k
13
votes
1
answer
9k
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 ...
user88
11
votes
6
answers
16k
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 ...
- 30.2k
47
votes
4
answers
10k
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 ...
- 2,555
11
votes
1
answer
2k
views
Of men and hats
There's an obvious generalization of this problem: There are a rather large number of prisoners, each of them seeing the color of the hat of all the following sad fellows bot not their; the hats may ...
- 2,087
80
votes
11
answers
23k
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.
- 5,701
25
votes
5
answers
4k
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.
...
- 698
23
votes
4
answers
8k
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 ...
- 9,072
16
votes
2
answers
4k
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 ...
- 4,179
15
votes
1
answer
5k
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 ...
- 5,718
14
votes
2
answers
3k
views
10 prisoners and 10 lists of numbers [duplicate]
10 prisoners are held captive by a cruel warden. One day he gathers them in the prison hall and tells them about a new game he wants to play:
"Tomorrow, I will assign each one of you a random ...
- 151
4
votes
2
answers
2k
views
A modified version of apples and oranges logic
Question: You have 3 baskets, one with apples, one with oranges and one with both apples and oranges mixed. Each basket is closed and is labeled with ‘Apples’, ‘Oranges’ and ‘Apples and Oranges’. ...
- 143
73
votes
9
answers
511k
views
60
votes
4
answers
83k
views
What is the maximum number of solutions a Sudoku puzzle can have?
I've seen Sudoku puzzles that can be solved two different ways. Referring to a traditional 9x9 grid:
Is it possible for a Sudoku puzzle to have more than two solutions? If so, what is the maximum ...
- 2,393
29
votes
3
answers
5k
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 ...
user88
23
votes
2
answers
676
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. ...
- 145k
23
votes
12
answers
184k
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.
...
- 351
14
votes
7
answers
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 $j$ ...
- 759
14
votes
1
answer
2k
views
Strategy for solving 0hh1 and Unruly?
Q42's game 0hh1 and Simon Tatham's game Unruly are two almost identical logical deduction games. In each one, we're given a square grid which is to be filled by tiles of two colours, and a certain ...
- 116k
13
votes
5
answers
4k
views
Labeling wires in a bundle
At a remote location, you just finished trenching a data cable across a large plot of land. The cable has 64 individual wires that are not color-coded or labeled.
You have a wire stripper, a simple ...
- 1,179
12
votes
7
answers
1k
views
Blue eyes riddle: what information is gleaned after the first night?
There are good explanations on this site and xkcd of the inductive reasoning leading to the riddle’s solution, but nowhere have I found an answer to the following aspect:
Exactly what information is ...
- 333
11
votes
3
answers
4k
views
Where has Jones lost 1 Rs?
Jack and Jones are brothers and they both sell apples for living. Jack sells 2 apples for 1 Rs and Jones sells 3 apples for 1 Rs. They each have 30 apples. Hence, Jack earns 15 Rs a day while Jones ...
- 639
10
votes
3
answers
2k
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 ...
- 2,131
10
votes
5
answers
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 ...
- 251
10
votes
6
answers
8k
views
Who has mud on their forehead?
This is probably my favorite puzzle. It uses logic, but it's not one of those "logic table" puzzles which i dislike immensely. What is this type of puzzle called and are there more like it ...
- 236
8
votes
2
answers
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 ...
- 5,123