# 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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### Can you solve this football league table problem?

Each team (A,B,C,D,E,F) plays each other once (on a neutral ground). Maximum number of goals scorable is 4. A team gets $3$ points for a win, $1$ point for a draw and $0$ points for a loss. At the ...
898 views

### The Troll, the dwarves and the gloves

A group of $N$ dwarves are caught by an evil Troll. As usual the Troll gives the dwarves a chance to escape if they solve a puzzle he created just for the occasion. Tomorrow morning each dwarf will ...
40 views

### Figure out the next two numbers in this sequence [duplicate]

1,11,21,1211,111221,312211,13112221,1113213211,....? Find the next two numbers in the sequence This question appeared in my math competition and I managed to solve it, and I will give a hint if ...
157 views

### Guess the numbers

One day Bob and Alice walk around they were having the following conversation: Bob: Alice go ahead and pick any random number. Alice: Okay, I have one. Bob: Alice multiply the random ...
340 views

### Next date with distinct digits

The date today is 7th June 2019, or 07/06/2019 (using the English DD/MM/YYYY ordering). When is the next date that when written in this way has all eight digits different?
133 views

### Is “meta”-logic valid for solving puzzles? [duplicate]

I think this question is best explained with a demonstration. In this case I'm playing a Range puzzle, but this kind of concept seems to work with other puzzle types too. Of interest here are the two ...
1k views

### A King's Hamiltonian Tours

a) Place the numbers 1 to 25 in the cells of a 5 x 5 board in such a way that consecutive numbers occur in adjacent cells either vertically, horizontally, or diagonally, and so do cells with numbers 1 ...
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....
149 views

### Just Another Sudoku for PSE

Crafted with love for PSE, <3
126 views

### The Mixed-Up Label [duplicate]

Mrs. Hudson had a rather large number of her extended family over for tea, and during this time a particularly mischievous great-nephew took the opportunity to wreak havoc in the kitchen. Seeing that ...
3k views

### Logic puzzle: Driving around the United States

For Super Bowl Sunday, here's a super-sized logic puzzle! This was a practice puzzle for a hunt I participated in a few years ago. There are ten delivery drivers driving around the United States of ...
226 views

### Double Chocolate: Happy Valentine's Day!

Hikouki (@flight_float) over on Twitter issued a challenge to make a Double Chocolate logic puzzle with a fixed grid pattern, and lots of logic puzzle makers responded to that challenge! Here's my ...
16k views

### Mensa Norway last 3 questions

I had no problems with solving first 32 questions from http://test.mensa.no but the last 3 questions are totally bugging me out even knowing the answers. Could anyone help me getting the logic behind ...
6k views

### Living next door to Alice

Bob and Charlie live in a small village with 99 houses, numbered from 1 to 99. One day they meet Alice, a person who has recently moved to this village. Bob asks her if her house number is a square ...
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. ...
545 views

### On The Subject of Blind Alleys

(This is part of a series of puzzles written for Timwi for a Secret Santa puzzle exchange, themed around various custom modules for the game Keep Talking and Nobody Explodes. No KTaNE knowledge is ...
872 views

### Using burning ropes as timer - how to measure 1 hour and 8 minutes with 3 ropes?

This is a variation of a well known puzzle, you can find the other versions on PSE. You have three ropes and a box with ten matches. As usual each rope takes one hour to burn completely when lighted ...
639 views

### Boat children and army crossing the river puzzle

During the war, a small detachment found itself confronted by a deep and wide river. However, they found a small boat in which two-children were rowing about. It was a very small boat and can only ...
776 views

### Welcome to the club

A financial manager of a bowling club, whose members are all couples (a man and a woman), creates three different membership lists. In the first list the couples are sorted by increasing age of the ...
404 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 ...
3k views

### What are the three numbers in this puzzle?

There are three people in a room without any equipment. Each one has a number on his forehead Every person knows the numbers the other two have, Every person knows that his number is either the sum ...
248 views

### Lenny’s Logical Internship

Lenny recently applied for an internship at Logicorp™, a company built around using logical reasoning to solve any sort of problems their clients face. The interview was long and difficult, and Lenny ...
452 views

### Setka - Complete grid using clues and sudoku-style logic; Theme - Halftime

This is a Setka puzzle; you can find more (along with a more detailed explanation of the rules) at our website, linked from our profile. How to play Setka, the short version: Answer each clue using ...
277 views

### Two shapes that cover a 4x4 grid with any 1x2 missing

Can you find two geometrical shapes with the following property: If you remove any 1x2 rectangle from a 4x4 grid, then the remaining area can be exactly covered with the two shapes. What do these two ...
272 views

### Missing No. 53 - Act 1: A Musty House

2/10/2020 Agent: Delta Flash Subject: William Plixer Age: 37 Gender: Male Appearance: Crew cut hazelnut hair. Round, blue eyes, snub nose, attached earlobes, and thin lips on ...
171 views

### How many ways could Alice have filled out the answer sheet? [closed]

Alice, Brie, Carlos, and Drake are taking a true/false quiz at school. There are four questions. The teacher was sneaky and made the answer to every question "true." Each person got a different score, ...
802 views

### Unbalanced weight of boxes

You are given a traditional balance scale with two pans (no reading) and 6 boxes with the following properties: 1) the weight of each box is a positive integer number 2) if you put any number of boxes ...
710 views

### Find a number based on lies about divisibility

A teacher writes a positive integer n < 50000 on the blackboard. The first student claims, that n is divisible by 2. The second student claims, that n is divisible by 3. The third student claims, ...
235 views

### Constructing an island according to rules in Smullyan's “What is the Name of this Book”

I've recently finished dropping my jaw at Raymond Smullyan's "What is the Name of this Book," and the section on Gödel's incompleteness theorem, involving islands of knights (truthers) and knaves (...
368 views

### 99 numbers on the blackboard

The numbers 1,2,3, ..., 99 are written on the blackboard. Alice and Bob play the following game, taking turns. Alice starts. At every turn, each player removes one number until two numbers are ...
148 views

### Setka - Complete grid using clues and sudoku-style logic

This is a Setka puzzle; you can find more (along with a more detailed explanation of the rules) at our website, linked from this user's profile. How to play Setka, the short version: Answer each ...
329 views

### Wizard's Labyrinth

A thief has snuck his way into the wizard's castle. After traversing a plethora of magical traps and illusory walls, he finally spies the wizard's hidden stash of gems beyond the end of a long ...
348 views

### Which is the missing number?

I am working on this puzzle since last week. 01 ?? 05 12 10 13 15 09 14 02 08 03 04 07 11 06 which is the missing number ?? note : answer is not 16
5k views

### Cover 63 squares of a chess board

Can you find 3 similar geometrical figures (common shape but can be different sizes) A, B and C with the following property: If you remove any square from a 8x8 chess board, then the remaining area ...
3k views

### House Number Mastermind

I was having a house-leaving party at my old house, and challenged four of my friends to guess the number of the new address, which had three digits. The responses I got were 280, 376, 304, and 370....
613 views

### Three shy fairies performing two thousand times

Three shy fairies participate in a dance competition. Since they are shy they don't want to be seen by anyone except for the five judges of the competition. The competition is composed of $2000$ ...
595 views

### One piece of a destroyed chess board

Once I met a friend and he told me the following story: I recently cut my wooden 8x8 chess board into different rectangular pieces along the edges. Each square of the chess board has a length of one ...
193 views

### Circular arrangement with professions and age based puzzle [closed]

Eight people, named A, B, C, D, E, F, G, and H; who work as a dancer, singer, lawyer, painter, doctor, teacher, architect, and professor; are 25, 40, 45, 29, 66, 24, 21, and 34 years old; although ...
1k views

### This new puzzle type needs a name {3}

I believe I have invented** a new type of puzzle... What is its name? ** Well, 'adapted' an existing one, really... Colour-blind-friendly version available here. Those without colour-blindness ...
466 views

### Pensive Nonogram - Two-Colour Puzzle

Fourth two-colour puzzle in the 32nd issue of Mega Pixel Puzzles by Puzzler.. I’ve made some progress, but I am stuck. Can you help me find my next move in it? (The puzzle is below)
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 ...
518 views

### Compoundoku wants BIG

Rules of Compoundoku: Solve both left and right Sudokus. In addition, the board below them is the Compound Board of both Sudokus. Each number on the Compound Board should tell either: (1) ...
297 views

### Can you open a safe with a lengthy complicated combination?

Two cousins were talking about their parents' safes. "They said I can keep my comic books in their safe, if I figure out the right combination, and enter it on the keypad correctly on my first ...
216 views

### Which figure is not needed in the pattern?

I have been trying to figure it out, but no logic so far. This question was given to me by the University of Sofia.
270 views

### wandering knight

Suppose a land with a finite number of castles. Each castle is connected (via roads) with exactly 3 other castles. One knight leaves from his castle and starts travelling. He moves in the following ...
1k views

### Introducing: Compoundoku!

Rules of Compoundoku: Solve both left and right Sudokus. In addition, the board below them is the Compound Board of both Sudokus. Each number on the Compound Board should tell either: (1) ...
115 views

### How to effectively hide an earth rebooter thingy [The Good Place Season 4 spoilers]

This puzzle is unsolved. I don't know if there is a solution or how to solve it. I'm also not sure what type of puzzle this would be, so if anyone wants to correct the tags, feel free. Imagine you ...
234 views

### What is the maximum number of allies that you can have in this scenario?

There is a military/diplomatic crisis, with many sides involved. Your goal, as an uninvolved party now entering the conflict, is to get as many allies as you can. You make an ally by supporting a ...