# 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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### One hat's number is the sum of the other 2. How did A figure out his hat number?

In the October 2003 issue of MIT Technology Review, Donald Aucamp offered this conundrum: Three logicians, A, B, and C, are wearing hats. Each hat displays a positive integer, and each logician can ...
196 views

### Superman looking for Supergirl

Superman needs to find Supergirl in a hotel room. Unfortunately, the hotel is also "super" and has 100,000 rooms arranged in a row. Each room has a door to the corridor and to the adjoining ...
2k views

### What is the maximum number of cities that can be destroyed?

As a commander of an army battalion, you have to plan the attack on some enemy cities which are connected by road-network. Before starting the attack, you have information about all the cities and ...
193 views

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### A colourful Colombian Sudoku

Fill the sudoku on the left so that each column, row, 3x3 box, and cells of the same color contain the numbers 1 to 9. The dots show how many numbers in the row or column of the grid on the right ...
409 views

### Lewis Carroll's Logic Problem: what do you know about great-grandsons?

This is from "Symbolic Logic, part 1 and part 2", by Lewis Carroll, edited by W.W. Bartley (1977), page 362: A man can always master his father; An inferior of a man's uncle owes that man ...
238 views

### Find the value of '?' in 4x4 table of numbers [closed]

Solve for ? 50 15 10 60 45 31 5 87 40 22 42 ? 9 4 3 14
689 views

### Tombs of Ancients

This is part 68 of the puzzle series Around the World in Many Days. Each part is solvable on its own. Dear Puzzling, The top grid here is a Yin-yang puzzle. Shade some cells in the grid so that ...
1 vote
573 views

### Prove that all 101 balls have the same weight

In a collection of 101 balls, each ball weighs a whole number of pounds. If any one is removed from the collection, the remaining balls can be divided into two groups of 50 balls each with the total ...
1k views

### Next date in the future such that all 8 digits of MM/DD/YYYY are all different and the product of MM, DD and YY is equal to YYYY

This problem is a little variation from this problem I made 2 months ago, which is inspired from this post. When is the next date in the future such that all 8 digits of MM/DD/YYYY are all different ...
127 views

### How to match pairs on raw tables?

The idea for the puzzle came from working with test score tables. In this case, the raw tables indicate an internal identifier that differs from user_id. To match, you have to download solutions and ...
1k views

### Finding a mystery number from a sum and product, with a twist

At a party of perfect logicians, Alzim and Era each select a positive integer and and report the number to Mufti. Mufti writes the sum of the two numbers on a card and the product on another card. ...
93 views

### What s the solution to the third pattern? [closed]

The values of the following two items are solved and you have to solve the third one according to the logics 27=SDD 91=QBI 43 =?
572 views

### What should the next step be in this Kakuro puzzle?

I have recently been learning more and more tricks for solving Kakuro puzzles, but I'm at a loss for how to solve the final bit of this puzzle. For reference, it is from the "Real Kakuro" ...
642 views

### Bulls and Cows meet Sudoku!

This is a Colombian Jigsaw Sudoku where the usual rules apply, but with irregular boxes. The dots in the right-hand scheme indicate how many of the numbers in a particular row or column are correctly ...
563 views

### Vacuum Salesman [duplicate]

A vacuum salesman rings on the door of a woman, trying to sell her a vacuum. The woman declines the continuous offers and gets annoyed by the persistent salesman. She eventually offers to buy a vacuum ...
218 views

### Finding a mystery number - with three logicians

Three perfect logicians named A, B and C each select a positive integer and report their number to Mufti. Mufti writes the sum of the three numbers on one card and the product of the three numbers on ...
1k views

### 66: Luftballons

This is part 66 of the puzzle series Around the World in Many Days. Each part is solvable on its own. Dear Puzzling, This is a Dosun-Fuwari puzzle. Place some balloons (white circles) and anvils (...
286 views

### Justifying a redouble

This puzzle is derived from a real game of bridge I played on Bridge Base Online. I was sitting North on board 9 (N dealer, E-W vulnerable) and the bidding turned out like this: West North East South ...
1k views

### Going around in circles

Solve the grid. Then solve the grid again. The answer can be one or two letters long.
1k views

### 3 doors guarded by 1 knight and 2 knaves

3 men are guarding 3 doors. 1 door leads to a pot of gold, while the other 2 lead to hungry lions. 1 guard always tells the truth, and the other 2 always lie. You are allowed to ask 2 questions in ...
175 views

### Generalized knights and knaves puzzle

A basic knight-knave puzzle (for the purposes of this question) takes the form $Q(n, s, k, x)$, where: $n$ men are guarding $n$ doors. The guards and doors are numbered for easy reference: Guard #1 ...
1k views

### Nonconsecutive Anti-Knight Fillomino?

Rules of Fillomino: Fill in all empty cells with numbers under the following rules. Divide all of the board into blocks. Fill each block with the same number horizontally or vertically. Each block ...
376 views

### The prisoners and the switch

After studying for a math exam some months ago, I fell in an uneasy sleep and had the oddest dream. I dreamt I was part of a company of soldiers captured in enemy territory, imprisoned for weeks. ...
1.8m 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, but the guards do know. One of the ...
343 views

### Culture Fair IQ Test

I took an IQ test on (https://www.psychologytoday.com/nz/tests/iq/culture-fair-iq-test) and encountered some questions which I wasn't able to solve: . Can anyone share their explanation for the above ...
478 views

### Oh no, my chocolate banana puzzles are not unique!

There is a hidden message (7, 2) inside the solutions of the nine puzzles. An answer will only be accepted if it correctly identifies said message. Here are the Chocolate Banana puzzle rules. Each ...
467 views

### The Room Of Tiles

You are stuck in a room with 100 floor tiles, and a magic button which you can carry with you. There are three types of tiles: real, fake and nopey. There are at most 49 fake tiles, and there is at ...
97k 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 ...
1k views

There is a population of people (finite or infinite). Any group of people (finite or infinite) in this population has someone assigned to be in charge of them. So someone is in charge of the whole ...
354 views

### Logical Reasoning - Seating Arrangement problem

Source P, Q, R, S, T, U, V and W are sitting around a square table in such a way that four of them sit at four corners of the square while four sit in the middle of each of the four sides. The ones ...
759 views

### Who is the murderer of Mr. Morgan?

The police have three suspects for the murder of Mr. Morgan: Mr. Hill, Mr. Spengler, and Mr.Gates. Hill, Spengler, and Gates each declare that they did not kill Morgan. Hill also states that Morgan ...
3k views

### Logic-grid puzzle. How do I have to interpret the clue?

There are eight students named Aman, Bobby, Chameli, Deepak, Ekta, Farook, Garima and Harsh in a school. They are in class 6th, 7th and 8th with no more than three students in any class. Each of ...
2k views

### What's the one digit you can fill in this partially hidden Sudoku?

A few weeks ago, I challenged some people to solve the puzzle I made. Two of them took it more or less seriously, but couldn't find the right solution. Now they are excited to see whether or not ...