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Questions tagged [logical-deduction]

A puzzle that needs formal logical deduction to arrive at a solution.

7
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2answers
4k views

Spatial IQ test puzzles

The following puzzles were created by Robert Lato to measure IQ in range between 160 and 190. Whats the solution to them? You are supposed to draw in the dented boxes what the missing figure is ...
8
votes
2answers
596 views

Middle weight puzzle

There are 100 white and 101 black balls. All the balls have different weights. Balls of the same colour look the same. White balls are numbered from lighter to heavier (from 1 to 100). The same is ...
11
votes
6answers
6k 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 that are ...
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. ...
14
votes
5answers
2k views

Church charity lottery

Suppose you've rigged the church charity lottery so that you cannot lose (what a swell guy you are). There are 10 drawings, and you start off with 10 dollars exactly. At each drawing, you must chose ...
5
votes
2answers
2k views

I have a pattern problem to solve!

The question reads: From the given pattern, What comes in place of '?'
7
votes
3answers
1k views

How do I solve the “Between Worlds” Android puzzle game?

I've been struggling for a while with the Between Worlds Android game, and have not yet solved it. I've only noticed a couple vague properties that hold in localized cases. To operate the puzzle, ...
8
votes
1answer
816 views

Number of tries to guess M-1 letters from M-letters-code

There are $N$ letters in an alphabet. There is a combination lock, the code to it consists from $M$ different letters. You can input $M$ letters combination and try to open the lock. (But you can't ...
8
votes
4answers
1k views

How to lock a shared artefact

This answer reminded me of a nice puzzle. I present it as a challenge for you. N thieves had stolen a magical artefact. They bought a lock with N keys and attached the artefact to a loop on a wall ...
17
votes
8answers
6k views

When to be sure that we have counted all the squares in such problems

My first question: how would one solve such problems (in general)? What should be the general technique? My second question: When to be sure that we have counted all the squares in such problems?
11
votes
1answer
3k views

How to solve this crazy Chinese puzzle for children?

I have been shown this "Chinese puzzle from textbook for 2nd grade" like a joke. But it is intriguing, so I would like to know the answer, but I am quite bad in associative puzzles and can't find the ...
16
votes
4answers
29k views

How to solve this IQ test puzzle with arrows and pied squares?

What is correct answer for this IQ task and why?
11
votes
8answers
9k views

Survive from death by asking the right question from trolls

You are in the intersection of two roads, there is a troll in the beginning of each road. One of them is liar (always lies), and one of them always tells the truth. One of the roads, ends to your ...
3
votes
2answers
651 views

How to generalise Partition of the pie for N envy people?

There is well known task: How to divide a pie between two people, so each will think that he got equal or more that the other one? It has the following solution: I know that it is possible to ...
28
votes
5answers
5k views

Two spies throwing stones into a river

There is a puzzle about two spies: Two spies must pass each other two secret numbers (one number per spy), unnoticed by their enemies. They have agreed on a method for doing this using only 26 ...
17
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 ...
19
votes
2answers
2k views

How to create a pure mathematical-logical based puzzle equivalent to resistance based physical puzzle?

I am thinking how to reformulate a physical puzzle in a way that it becomes purely logic based (doesn't uses physical lows and can be solved by a person, who knows nothing about physics). The puzzle: ...
22
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 ...
21
votes
3answers
3k views

Winning an unfair game

I came across the following interesting problem today: A game consists of a sequence of plays; on each play either you or your opponent scores a point, you with probability $p < \frac{1}{2}$, he ...
16
votes
1answer
2k views

You are a cat. How do you swap?

Number twenty-one cages containing mice, 1, 2, 3, etc., up to 21, and place them in the following order: 1 14 15 17 3 7 13 6 20 2 19 21 5 18 8 11 16 9 12 4 10 ...
23
votes
4answers
6k 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 ...
24
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 ...
13
votes
2answers
4k views

Is it indeed impossible to score any points in the test in Heinlein's “Space Cadet”?

In Heinlein's Space Cadet, one of many tests administered to the protagonist seems to have no way of scoring any points. See the excerpt below. Late in the day he was ushered into a cubbyhole ...
5
votes
1answer
784 views

Clock Puzzle problem

Today I came across this puzzle: How many minutes is it until six o'clock if fifty minutes ago it was four times as many minutes past three o'clock? Any help?
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2answers
3k views

Are there any forms of patience or solitaire that can be solved by logic alone?

Single player games using a single deck of playing cards often called patience or solitaire, generally involve a degree of skill and luck to solve, with card shuffling ultimately being the deciding ...
10
votes
2answers
1k views

When and where was the first logic-grid-based puzzle published?

Logic puzzles with a set of conditions and a "logic grid" are very popular. More than one publisher is currently producing puzzle books with these types of puzzles. A Wikipedia article claims ...
61
votes
25answers
13k 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,...
6
votes
1answer
3k views

Are there 'Hexanum' puzzles that require advanced methods to solve? [closed]

The puzzle below features each week in a TV guide. It's called "Number Workout" there but I've done a bit of research and it seems to be called "Hexanum" elsewhere. It bears some resemblance to Sudoku,...
12
votes
4answers
3k views

The Mexican Standoff

There are three cowboys in a Mexican standoff against each other, named Juan, José, and Jorge. Juan is the straightest shooter in the West, and can hit his target 100% of the time. José, who has a ...
15
votes
1answer
5k 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 ...
43
votes
6answers
27k 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 ...
1
vote
1answer
546 views

Could a gold/{second metal} crown the be created that would pass the Archimedes test cost effectively? [closed]

Many people are familiar with the story of Archimedes submerging a crown in water to identify if the volume of the crown was consistent with the volume of the same amount of gold. The test was to see ...
43
votes
3answers
10k 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 ...
153
votes
22answers
67k 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 ...
23
votes
5answers
4k 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?
20
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 ...
8
votes
4answers
2k views

Guessing hat colors

Red or Black There are 3 children sitting on three chairs. The children can only look forward and all wear one hat. The hats are either black or red. They are a total of 5 hats, 3 are colored red and ...
38
votes
5answers
5k 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....
28
votes
3answers
4k 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 ...
12
votes
4answers
4k views

The Puzzle of the Locked Box

Here's an old puzzle I found in a book once. A box has some number of locks on it. It is guarded by a Grand Vizier and four slaves, each of which hold keys to the locks. The Grand Vizier and ...
9
votes
3answers
2k views

Sliding Bolt Puzzle - fastest solution (time-wise)

This is a follow-up question for the Sliding Bolt Puzzle. If you have not solved it yet, you might want to head there first, as the extended discussion of its solution in this question will contain ...
5
votes
4answers
1k views

Round-Robin Tournament

20 teams played in a round-robin tournament. The winner of each game got 1 point, and the loser got 0; there were no draws. Each team's total score was a square number. At least one team had a unique ...
13
votes
5answers
4k 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. ...
48
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. ...