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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2answers
2k views

Someone has vandalised this long division. Can you reconstruct it?

Oh dear, someone has vandalised this long division. They've replaced every digit either with a wrong digit or a hyphen. Your task: reconstruct the entire thing. There's no remainder. Please show ...
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2answers
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Math logic Triangle

Rules Arrange numbers from 1 to 15 to the white triangles. A op B = result Green triangle means 2 numbers of its side are adjacent numbers. (-) means find the difference (/) means divide the bigger ...
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4answers
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Past, Present and Future

There are 3 gods, named Past, Present and Future, who all look identical. They sit in a throne room, with one in the middle, the others on the right and left. You are allowed to ask them a series of ...
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2answers
2k views

True-False Examination

Alice, Bob, Chloe and David took a 10 question true-false exam; every correct answer of a question is $1$ point. Their answer sheet and the result is shown as below: So what is David's total ...
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6answers
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Pursuit Problem: Mutineer trapped on an island

You are a pirate. One of your crew ran off in the night, swam to your secret island, and dug up your life's treasure. You need to capture her. You may deploy $n$ pirate ships to patrol the boundary ...
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1answer
1k views

Rearrange the Sentences, Cross out the Wrong One, Fill in the Blank, and… Do Some Logic!

Introductions 1. Rearrange the sentences below into a good conversation! Alice: Hi Bob, how are you? Alice: I'm fine too, but my school kinda sucks. Bob: And how about you, how ...
18
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1answer
917 views

A Total Masyu puzzle

In a Total Masyu puzzle, one must draw a single loop through the centres of some cells according to the following rules: The loop may only travel horizontally or vertically, never diagonally; all ...
18
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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: ...
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17answers
13k views

If this were an answer, what would be the question?

Heading down to the city of Thebes, you encounter a Sphinx who stops you in your journey and speaks to you. The Sphinx has a riddle for you: if you can solve it, she will let you pass; if you fail, ...
17
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8answers
4k views

Infinite precision

The man tells you, "To enter the door of infinite precision, you must complete all of these tasks perfectly: Hold in front of me a baby that is exactly two days old. Bring me a metal object that ...
17
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2answers
2k views

We are two immediate neighbors who forged our own powers to form concatenated relationship. Who are we?

Our concatenated number is $ \overline{ABAC}, $ where $ A, B, C $ are all positive digits (1 - 9). Our relationship is $$ \overline{ABAC} = A^A + B^B + A^A + C^C $$ Who are we?
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10answers
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Communicating Information about Cards

Seven cards, numbered $1,2,3,4,5,6,7$, are distributed randomly among three people: Rand gets one of them, Deusovi gets three of them, and Gareth gets three of them. All three know what the seven ...
17
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2answers
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Find the missing piece

One day I got a paper from my courtyard with the center portion missing. Here is what the poster looks like: I have made some pieces of paper so that I can stick one to the center of the poster. ...
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3answers
6k views

Which two students spoke wrongly? [duplicate]

A teacher wrote a large number on the board and asked the students to tell about the divisors of the number one by one. The 1st student said, "The number is divisible by 2." The 2nd student said, "...
17
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4answers
800 views

Constructing interesting “Don't Know - Don't Know - Now I know!” type puzzles

The professor has a piece of hidden information $C$. Alice is given an envelope containing information $A$, Bob is given information $B$. It is possible to deduce $C$ from $A$ and $B$. The ...
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6answers
2k views

Abby and Bobby and three numbers on the blackboard

Abby selects a non-negative integer $A$, and Bobby selects a non-negative integer $B$. They then both tell their number secretly to Summy. Summy writes the numbers $5$, $8$, and $15$ on the ...
17
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3answers
395 views

Is $s$ larger than the radius of circumscribed circle?

In the figure, showing a square and an equilateral triangle, is $s$ larger or smaller than the radius of the circumscribed circle?
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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?
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5answers
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Statements that the deities True and False cannot say

You over exert yourself working on logic puzzles and die of exhaustion. You are awoken by the omniscient deities True and False. True only speaks true statements and False only speaks false statements....
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6answers
6k views

A death at a restaurant

You are a mafia leader and because of mysterious recent developments, you had to call the meeting of heads which is happening right now at your's cousin restaurant. The problem is, after the opening ...
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5answers
2k views

Bizarre Love Triangle

I work in quite an unusual office. Everybody who works here has a colour for their surname! It’s a bit like that old board game Cluedo, except nobody has been murdered. Still, there is a bit of a ...
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2answers
2k views

Fairy Chess #1- The Mastermind

(Fairy chess is a general term for any kind of chess variant with pieces that aren't used in the normal game) (Inspired by The Black Prowler (chess)) In this variant, white has their entire army ...
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2answers
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Equal queens in every aspect

It is asked that you place $12$ queens on a $5$x$5$ chess board so that every queen can see the same number of empty squares. For the purposes of this puzzle, a queen can see any square on ...
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4answers
2k views

Can anything be deduced from the statement “If I am a truth teller, the other two are liars”?

There is a scenario which goes along the following lines: There are three friends. The friends are either truth tellers, or liars. One friend makes the statement: "If I am a truth teller, the ...
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3answers
2k views

Two brothers, two watches

Two brothers, Jack and Joe, were born in May. One was born in 1932, and the other, a year later. Each brother owned a watch, which was previously possessed by their father. Considering their age, ...
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5answers
3k views

Help me, I hate squares!

There is $5$x$5$ equidistance matrix dot given as below; You need to remove dots from the figure where it will be impossible to form a square by drawing lines between dots at the end. So what is ...
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2answers
2k views

How to solve the next field of this Kenken-Puzzle by logic?

First of all here is the spoiler free Kenken-Puzzle for everyone who likes to solve this on her/his own. Now here is how far I come with this, but now I struggle a lot. What I am looking for is only ...
17
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5answers
1k views

Again! 6 prisoners, 2 colors, one mute

After that last game, the warden didn't like that they escaped. So he made them all play again. Like before, they know there are 6 prisoners, 3 red hats and 3 white hats. They know one prisoner is ...
17
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4answers
423 views

The Djinni, the Marid and the Oracle (working title) :P

Although I like this puzzle, I'm still fairly new to this site and I've never tried to write one like this before. I think it may be a little too long, a bit too easy and some of the spelling and/or ...
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1answer
2k views

Finally, you wake up from a coma

You can barely open your eyes when a doctor walks up to you: You are a lucky one. Not many people have survived an accident like this. Only a handful of neurosurgeons are able to perform such an ...
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3answers
2k views

Star Puzzle: Determine which circles are True and which circles are False

A circle with number x means: “This circle is connected (straight line) to x circles with a true statement” This is valid only if the statement in the circle is True. If a circle is False, ...
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3answers
2k views

Mutation of aliens

In the image you can see twelve mutation chambers (A to L). Each alien on the left side of the aliens goes through the three mutation chambers of its right side. The alien on the right side is the ...
17
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1answer
1k views

Sudoku with only 8 predefined numbers

Have fun with my self-made Sudoku puzzle. Solve this Sudoku puzzle using the standard Sudoku rules: Fill any row, column and bold-framed area with the numbers 1 to 9. Hint: It is not as difficult as ...
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9answers
1k views

Agent 001's faulty delivery box

There are 10 agents living at their respective homes. They used a secret mailing system that sends one box at a time, but it is now spoilt. Now, it functions as follows: It counts the number of ...
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3answers
2k views

Lies, damned lies, and statistics

A (hopefully) new variant on the Knights & Knaves problem. On the island of D'Israel, the inhabitants fall into three types: Liars, Damned Liars, and Statisticians. They are visually ...
17
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1answer
913 views

Farm dimensions

Here is a question I was given during an interview a few years ago. There was a farmer who had two daughters. One day he was considering giving his farm to his girls. He took his first daughter, ...
17
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1answer
2k views

The Pirates of Beal Isle - very long logic grid puzzle

Story Let me tell ye a tale: Somewhere northeast o' the Bahamas there be a tiny scrap o' rocks stickin' up out o' the sea known as Beal Island. It be a barren, rocky place, and no man ever called it ...
17
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1answer
441 views

Flying pigs arrive

You’ve built pens for flying pigs. Being, well, flying pigs, they pick their own accommodation in full accordance to their preferences. Can you figure out what creature joined them? Pigs only occupy ...
17
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1answer
500 views

Octagonal Kurotto

This is a Kurotto puzzle. Rules of Kurotto: Shade some cells to form connected groups of shaded cells. Circled cells are unshaded. If they have a number in them, that number tells you the sum ...
17
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1answer
432 views

Awesomism and its awesome gods

Recently, I dived into a nice religion of Awesomism. It is pantheic, with a lot of difficult relations between gods. Twelve gods of Awesomism are split between four pantheons: Gods of cunning: Liar, ...
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5answers
1k views

100 Prisoners' Names in Boxes - Save them all!

This puzzle is based on 100 Prisoners' Names in Boxes: Names in Boxes The names of 100 prisoners are placed in 100 wooden boxes, one name to a box, and the boxes are lined up on a table ...
17
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1answer
362 views

Diabolical Deceptions: A 333rd Birthday Tribute to J.S. Bach

Johann Sebastian Bach is one of the most famous composers from the Baroque period. If he was still alive today, he’d be 333 years old. So, let’s celebrate 3 of his most famous works with a 33x33 loop ...
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3answers
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Names of Physicists Problem

This problem has been vexing me all day. It comes from an old IQ test. Note that while the test says not to discuss the problems on it in order to maintain its integrity, the test itself closed years ...
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1answer
592 views

Middle out: A puzzle that won't behave

Ah, jeez. You'd think making puzzles was easy. What kind of fool thinks he can turn up and instantly turn in a working puzzle on his first try? I've been checking my pocket calculator and rolling die ...
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9answers
7k views

Salesman's claim for mechanical keypad lock - 5 buttons and 545 combinations!

A company makes mechanical keypad locks. The keypad is a set of five buttons arranged vertically. O O O O O The buttons are quite close together. Once a ...
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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 ...
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2answers
2k views

Blind Person Ball Game

You are blind and your friend presents you with 6 equal balls of which 3 are red and 3 are green. You friend challenges you to game to find a green ball. You must select 3 of the balls and your friend ...
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4answers
31k views

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

What is correct answer for this IQ task and why?
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3answers
3k views

Which lorry is carrying drugs?

Five lorries are parked in a French layby, having recently come off the ferry at Calais. The police know that the lorry headed for Lisbon is smuggling drugs, but they're not sure which one it is. All ...
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3answers
2k views

Four buttons on a table

I was asked lately (in an interview) to solve this puzzle, which is similar to the 4 cups on table puzzle. In a certain room there is a rotating round table, with 4 symmetrically located ...