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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19
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2answers
2k views

Heyawake: An Introductory Puzzle

This is a Heyawake ("divided rooms") puzzle. Rules of Heyawake: Shade some cells of the grid. Shaded cells cannot be orthogonally adjacent; unshaded cells must be orthogonally connected. ...
19
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7answers
3k views

When was Alice Born?

This is inspired by the following recent question: Living next door to Alice Having failed to figure out where Alice lives, Bob and Charlie endeavour to determine the month in which Alice was born. ...
19
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3answers
2k views

Which two houses didn't get any mail that week?

Postman delivers the mail in the small village. This village has exactly ten houses, numbered from 1 to 10. In a certain week, he did not deliver any mail at two houses in the village but at ...
19
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8answers
2k views

30 fake coins out of 99 coins

You are given 99 coins which consists of 30 fake ones. You also have a digital balance scale with perfect precision that shows how much difference between weighs you put on. For example, if you put 10 ...
19
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4answers
2k views

Escape The Strange, Code-Filled Cave

You awake in a weird cave with something strange written on the wall. You find a small piece of paper on a rock. It says the following: Solving each code and entering it into the password entering ...
19
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2answers
941 views

Tic tac toe - Sudoku: A variation in which the centre box defines the layout of the other boxes

I stumbled across this interesting variation of Sudoku the other day and thought I'd give it a try, it has however baffled me and I've been unable to progress past the very early stages. The puzzle ...
19
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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, ...
19
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2answers
581 views

Deer-hunting in Mesak

The following are ten sentences in the Mesak language: ...
19
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5answers
2k views

Find the 8-digit number

A secret number has each one of its 8 digits colored either blue or red. Here are some clues: 1. All digits from 1 to 8 appear in the number. 2. The first two digits are not consecutive. 3. The ...
19
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6answers
2k views

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 ...
19
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1answer
727 views

Numbered Logicians near the Blue Eyes island

There is an island near the famous Blue Eyes island where 100 perfect logicians live, each with a number between 1 and 100 (repetitions allowed) tattooed on their forehead. They know all the numbers ...
19
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1answer
6k views

Can you solve this logic puzzle in disguise? The color code behind the tomb

Another themed puzzle for you to enjoy. As with all my puzzles, please provided feedback about pro's and cons of the puzzle. The puzzle is self-contained (the link is just to provide a theme) and I ...
18
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9answers
1k views

One-one communication

5 people are standing in a circle - person A needs to tell his salary to person B, but none of the others should know A's salary. How is this possible, if every person only whispers to the person on ...
18
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6answers
4k views

Guess five binary digits!

Person A thinks of a 5 digit binary number. Person B tries to guess the number. B can guess a 5 digit binary number and A will respond with the number of correct digits (digits in the right place). ...
18
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8answers
3k views

What Imprisonment sentence will immortal citizen soldier Guilt receive?

On planet Immortal, everyone lives forever but essential resources (including food and supplies) on the planet are limited. Ultimatopian raiding swords are the most effective weapon available to loot ...
18
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4answers
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 ...
18
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6answers
2k views

Can YOU guess this Riley Riddle?

My Prefix returns us to the dark ages. My Infix belongs to someone. My Suffix has annoyed me since birth. Hint 1: Hint 2:
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3answers
3k views

Binary Minesweeper

This Puzzle is a form of the classical MS Minesweeper which keeps popping into my head. In Minesweeper, a 2D grid is filled with mines and numbers whereas each number represents how many of its 8 ...
18
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8answers
2k views

When should you rest?

You are in an airport and are worried about missing your flight. So you start to run the long distance to the flight gate at a steady speed of 10km/h (you have bags and are not very fit). Luckily ...
18
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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 the truth, ...
18
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5answers
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. ...
18
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5answers
2k 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 ...
18
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2answers
1k views

Miss Toad and her frogs

Miss Toad owns a lot of frogs. These frogs are all looking the same, but they can be either mad or nicely. If a mad frog is in a room with 3 nicely frogs, then he turns red, because he is ashamed. ...
18
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2answers
931 views

Find the safe path through the dungeon!

You need to get from the bottom to the top. But this dungeon puzzle is extremely ancient, and unfortunately, the symbols on the tiles are no longer visible. Stepping on an unsafe tile means certain ...
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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
2k views

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
2k views

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 ...
18
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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 ...
18
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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 ...
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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
438 views

A special soccer tournament

30 soccer teams participate in a tournament. Each team plays against every other team exactly once. For a victory a team gets 2 points, for a draw 1 point and for a defeat 0 points. At the end of the ...
18
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1answer
1k 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
votes
1answer
398 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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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
15k 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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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 ...
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?
17
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10answers
1k views

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 ...
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2answers
3k views

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. ...
17
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4answers
864 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 ...
17
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6answers
3k 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
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
2k views

Paint 21 Squares of a 7×7 Board Without Forming a Rectangle

Got a nice puzzle from my friend, when he was competing in IWYMIC/IMC 2011. Paint $21$ of the $49$ squares of a $7 \times 7$ board so that no four painted squares form the four corners of a rectangle....
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4answers
32k views

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

What is correct answer for this IQ task and why?
17
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3answers
405 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?
17
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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
4k views

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 ...
17
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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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