# 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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### 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
1.2m 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 ...
86k 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 ...
7k 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....
11k 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 ...
6k 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. ...
32k 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 ...
1k 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 ...
603 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 ...
18k 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,...
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 ...
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 ...
6k 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 ...
14k 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 ...
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, ...
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 ...
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 ...
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 ...
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 ...
875 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 ...
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 ...
6k 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. ...
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 ...
7k 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)...
13k 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 ...
7k 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 ...
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 ...
8k 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 ...
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 ...
22k 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.
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 ...
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 ...
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 ...
2k views

### In the blue-eyes puzzle, why can't they skip ahead? [duplicate]

In the solution to the Blue Eyes logic puzzle, there is a follow-up question: Each person knows, from the beginning, that there are no less than 99 blue-eyed people on the island. How, then, is ...
4k 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 ...
640 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 ...
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’. ...
498k views

### Crack the lock code

Does any one know how to crack this? I got this as a challenge.
176k 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....
7k 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 ...
579 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. ...
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 ...
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 ...
1k 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 ...
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 ...
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 ...
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 ...
16k 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 ...