# 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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### 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 ...
68 views

### The king, the princess, the 3 wise men, and the 3 x's [duplicate]

A princess just became of marriageable age, and her father went out to get 3 wise men. He placed them at a round table and wrote either an X or an O on each of their heads, writing in such a way that ...
4k views

### Men digging holes

Suppose 9 men take 9 hours to dig 9 holes in the ground. (a) How many hours would it take 3 men to dig 3 holes? (b) How many men would it take to dig 54 holes in 54 hours?
2k views

### How to solve Rubik's Cube using mathematical formulas? [closed]

I am trying to solve Rubik's Cube, but it took one month for me when I started. Are there any mathematical formulas, rules and tips for solving Rubik's Cube in less time (i.e. minutes)?
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### Sudoku embedded in a Kakuro

In addition to standard Kakuro rules, the grey shaded cells must form a valid Sudoku solution. One sum in this puzzle has been corrected from 28 to 23. Fortunately, it was in a location that nobody ...
165 views

### The Death Recording

A woman was found dead in her house. She lay slumped on her desk, holding a gun in her hand. A cassette tape recorder was on her table. The police on entering the house saw the cassette recorder and ...
2k views

### Find two coins using a balance scale

You are given 20 identical coins. 18 of those coins have a weight of 10g each, 1 coin has 9g and 1 coin has 11g. You are given a traditional balance scale with two pans (no reading). What is the ...
1k views

### 2 crates and 2 logicians

Two perfect logicians (A and B) each have a bag of gold coins. A has more coins than B and each bag contains an amount of coins which is some multiple of 6. All coins are identical in appearance and ...
228 views

### The Train and The Cyclist [closed]

A railway track runs parallel to a road until a bend brings the road to a level crossing. A cyclist rides to work along the road everyday at a constant speed of 12 miles per hour. He normally meets ...
2k views

### Measure the diagonal of a brick

You are given three identical bricks (cuboids) and a ruler (scale) as shown in the figure. You have to find the length of the brick's diagonal without using any formula and by using the ruler only ...
415 views

### Backwards Boggle

I came up with a fun little 1-player puzzle for myself to do when bored. Pick 5-6 words, preferably words that share a good number of letters, and try to create a Boggle board containing all of those ...
290 views

### Density-type puzzle: Having A Good Day?

Here's another Density puzzle. I've got to say, I really like making these. Part of this is pretty simple, and part of it is much more complicated. Let's see what happens! Here it is: Solution: (3,1,...
4k views

### Three people wearing hats

Ms. Doha gave hats with different non-zero single digits (two of which are factors of the third) to Ms. Haha, Ms. Lola and Mr. Hehe. The three of them can't see the digits on their own hat though they ...
162 views

A thief plans to break into a castle, but unfortunately, it is surrounded by a moat that the thief cannot possible swim through. The only way they can hope to get in is through the main entrance, ...
1k views

### Reconstructing the results of a 6-team soccer tournament

6 teams played in a "round-robin" soccer tournament, in which each team played each other team once. Each game had 3 possible outcomes: team 1 won, draw, or team 2 won. The winning team received 3 ...
27k views

### Two doors with three guards - one lies, one tells the truth, and one is unreliable

This is an extension of Two doors with two guards - one lies, one tells the truth, but in this situation you are a prisoner in a room with 2 doors and 3 guards. One of the doors will guide you to ...
314 views

### What's that puzzle that goes like: Person A never lies, Person B always lies, etc?

What's the name of the puzzle where you're given something like: Person A never lies. Person B always lies. Person C I don't remember. Then it continues like: Person A says that person B is ...
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### 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, ...
762 views

### Reconstructing the results of a 5-team soccer tournament

5 teams are playing in a "round-robin" soccer tournament, in which each team plays each other team once. Each game has 3 possible outcomes: team 1 wins, draw, or team 2 wins. The winning team receives ...
76 views

### A spy in Fruitland [duplicate]

The army of the big and violent-prone country of Fruitland is planning to launch a nuclear rocket that could possibly destroy the near pacific little country of Vegetablesland. It is well known that ...
170 views

### A Coldport Christmas puzzle

Detective Inspector Playfair, an energetically boisterous policeman who often complained about Endeavour Morse having his own TV show, was sat on a bench at the side of Coldport's newly laid town ...
299 views

### How many eyes do we have? [closed]

If a giraffe has two eyes, a monkey has two eyes, and an elephant has two eyes, how many eyes do we have? The question is not guess work.. it has definite answer.
390 views

### A box full of unfair coins

Lolek and Bolek are arguing on whose turn is to take out the trash. They have a box with $n$ coins. when the coin $i$ is thrown, the probability that it lands on heads is $p_i$. They decided to make ...
357 views

### Tile-laying for beginners

Coldport is celebrating having a new town hall by laying a tiled design in the public square in front of the building. The design is also square: $5\times 5$ tiles square, in fact, and features three ...
127 views

### Find the lowest floor from which Venus eggs break [duplicate]

Venus gave you two eggs because she wants to test their strength. She lives in a 100 floor building and she wants to find the first floor above which the eggs break when thrown out of the window. ...
148 views

I think there must be a way to solve this but I can't get there Green + Blue = Yellow Red + Green = Purple Yellow - Purple = Red Red + Green + Blue = 9 I have made some progress And but I run ...
126 views

### Perambulating ants 2

The ants from this puzzle have been placed into a new arena: a cross-shaped hallway with a pillar (black square) in the centre and four statues (numbered 1-4) set symmetrically. The ants, like last ...
940 views

### Super Secret Cookbook

You requested the password for a super secret cookbook and received an SMS with the following content: 77733666688833 2555555 777772222337777 2663 777337555222233 84433 6688622337777777 9444844 ...
152 views

### 8-puzzle in 12 steps

This quiz is about the 8-puzzle. It is a board with 9 spaces. There are 8 tiles with the numbers 1 through 8. One space is empty (.). You slide the tiles around the ...
808 views

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### XKCD inspired logic puzzle

I came up with a logic puzzle inspired by this xkcd comic. I don't yet have an answer, and I am wondering if anyone can come up with one. You are in a room with three doors. Two of the doors lead ...
14k views

### They use me… What am I?

I'm complex inside,but easy on the outside. I'm loud for one,but quiet for others. I'm used to getting hit,but there's no alternative. I die as fast,as I rise again. What am I?
191 views

### Blood Type Puzzle 2: Am I Pure Blood?

This puzzle is similar to the first puzzle but with a few twists: In this question: both my mom and I are blood type B. But this time I don't know my dad's blood type. My mom said her parents ...
503 views

11k 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 ...
232 views

Request of me twenty, receive of me twenty. Request of me sixty, your behest will be fulfilled. Request of me eighty, you'll be given the same; but ask for one hundred, and you will get only sixty. ...
737 views

### Queens full of jacks

(Note: I doubt that this puzzle is complex enough to post it here, but I still took a try.) There are 3 queens and 2 jacks (a full-house combination from poker) taken from a deck with standard suits, ...
10k views

### How can I convince my colour blind friend that his two balls have different colours?

This question is inspired by this one, inspired by another Stack Exchange network question. My colour-blind friend has two balls, one red and one green. However, he is convinced that they are the ...
8k views

### The Harry Potter Potions Riddle

A simple riddle from the first Harry Potter book. You are in a room with seven potions. There is a doorway ahead and a doorway behind, both engulfed in flames. Which potion will allow you to move ...
35 views

### Using a balanced scale find the minimum and maximum weight of items [duplicate]

There are 1567 items with different weights. The goal is to find the item that has the maximum weight out of the 1567 and the item that has the minimum weight out of the 1567. For this you are allowed ...
4k views

### A simple murder mystery puzzle that I came up with

A woman was found dead in her apartment. She was hanging from the ceiling but the detectives deduced that it was not suicide because of the bruises on her body (indicating a struggle) and the mess in ...
1k views

### A fish story on aymara language

Interesting story I stumbled upon: Aymara is a South American language spoken by more than 2 million people in the area around Lake Titicaca. Among the speakers of Aymara are the Uros, a fishing ...
543 views

### 2 fake coins from a pile of 30 coins

You need to find two fake coins from a pile of 30 coins. You know that a fake coin has a different weight to a real coin, but you don't know whether it is lighter or heavier. You also know that all ...
2k views

### 2 Person Same Number Verification

Alice and Beth both receive a random integer from 1 through 10, inclusive. They only know the number that they are given. The two of them want to come up with an algorithm to check that their ...
224 views

### Turning a fan on

I bought an air purifier which has [off, low, medium, high] settings and a single button. If it is on, the first button press activates the lights and subsequent presses increment the level with off ...