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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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8 votes
3 answers
988 views

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 ...
2 votes
2 answers
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 ...
5 votes
2 answers
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 ...
3 votes
1 answer
193 views

Flea in six boxes

A flea is hiding in one of six boxes. To find the flea you can open a box (which cost \$1). If you did not guess correctly, after closing the box, the flea will jump randomly to a neighboring box to ...
0 votes
2 answers
159 views

Weighing Coins -- a Different Approach

This is a question of my own devising. You have a double pan scale which will tell you whether 2 coins or 2 groups of coins weigh the same or whether one side is heavier than the other side. You have ...
4 votes
1 answer
340 views

Largest prime number erroneously erased when finding all primes less than 1000 [closed]

Chicharron is a lover of mathematics and once wanted to find all primes less than 1000. He did by the following steps below: He wrote all the numbers from 2 to 1000. He circled the number 2 and erased ...
3 votes
1 answer
331 views

5 guards, and get rid of the timer!

I like the lies and statistics question, but it is a bit too violent, so I suggest a (slightly harder) and way less violent version. You are looking at the basement of your house, and you see three ...
7 votes
3 answers
1k views

Green Eyed Oracle Variant - Not a Multiple of 17

100 perfect logicians have been gathered on an island. It is common knowledge that logicians always have blue or brown eyes, though on this island, all eyes are blue. However, there are no reflective ...
3 votes
3 answers
565 views

Knights, Knaves, and Spies [closed]

I need help understanding this problem. An island has three kinds of inhabitants: knights, who always tell the truth, knaves, who always lie, and spies, who can either tell the truth or lie. You ...
0 votes
1 answer
100 views

Identify the truth teller, the liar and the spy

Beginner puzzle This puzzle is intended to be suitable for people who are new to puzzle solving. Clarification: Both experienced solvers and new solvers are welcome to post solutions to this puzzle. ...
7 votes
1 answer
375 views

Colombian Sudoku, Cows and Bulls again…

Fill the sudoku on the left so that each column, row, box, and colored box 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 ...
30 votes
1 answer
4k views

Are you radical enough to solve this SURDOKU?

All "surds" represent whole numbers smaller than 15, and the same number is never used twice with the same index. (It's a sudoku.) Attribution: PUZZLEBOMB.co.uk. Puzzles by @stecks & @...
4 votes
3 answers
822 views

Eliminate some numbers so that each of the three rows contains the numbers 1 through 9 each exactly once

Beginner puzzle This puzzle is intended to be suitable for people who are new to puzzle solving. Clarification: Both experienced solvers and new solvers are welcome to post solutions to this puzzle. ...
10 votes
2 answers
577 views

Fill the triangular grid using the digits 1-9 subject to the constraints provided

Fill the grid using the digits 1-9 four times each. No row or column can contain the same digit more than once. The total of each row and column is provided, as well as clues to the numbers forming ...
2 votes
1 answer
192 views

What is the name of this puzzle type? How to create one? nxn grid where you select n cells with different numbers

I want to create a specific puzzle, but I'm wondering if it already has a name, and if I can find some pointers on how to make it hard. I have a NxN grid filled with numbers going from 1 to N. I want ...
14 votes
3 answers
803 views

Fill the grid subject to product, sum and knight move constraints

Using the numbers 2, 3, 4, ... 19 each exactly once, fill some of the empty squares in the grid with a number so that the product of the numbers in each row is as shown, as is the sum of the numbers ...
1 vote
1 answer
146 views

Next date in the future that satisfies the following conditions

When is the next time that a date will satisfy the following conditions: YYYY days from MM/DD/YYYY is also the (DD)th day of a month. Note that YYYY stands for the year. All eight digits of MM/DD/...
1 vote
0 answers
99 views

Why math is hard to understand or explain in reverse [duplicate]

Three people go into a restaurant and each of us has \$10. So we start with \$30. The bill comes to \$25 which means there is \$5 left over. Out of that \$5 we each take back \$1 (which would be \$3 ...
7 votes
1 answer
168 views

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 ...
3 votes
2 answers
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 ...
2 votes
1 answer
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
15 votes
1 answer
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
5 answers
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 ...
13 votes
1 answer
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 ...
-1 votes
0 answers
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 ...
18 votes
3 answers
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. ...
2 votes
0 answers
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 =?
6 votes
1 answer
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" ...
8 votes
1 answer
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 ...
0 votes
2 answers
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 ...
2 votes
2 answers
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 ...
18 votes
1 answer
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 (...
3 votes
2 answers
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 ...
17 votes
2 answers
1k views

Going around in circles

Solve the grid. Then solve the grid again. The answer can be one or two letters long.
3 votes
6 answers
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 ...
3 votes
1 answer
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 ...
18 votes
2 answers
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 ...
9 votes
3 answers
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. ...
136 votes
16 answers
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 ...
3 votes
1 answer
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 ...
5 votes
1 answer
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 ...
5 votes
1 answer
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 ...
197 votes
26 answers
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 ...
26 votes
3 answers
1k views

Leaders and Rulers

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 ...
2 votes
2 answers
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 ...
3 votes
2 answers
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 ...
-2 votes
2 answers
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 ...
16 votes
1 answer
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 ...
7 votes
1 answer
480 views

Triple Homicide Sudoku

You are a special consultant who is brought in only for the toughest of cases. A serial killer has been on the loose and has struck the first day of the month for three months in a row now. Interpol ...
3 votes
1 answer
184 views

Long Division when it is almost, but not entirely, wrong

Hmm, my last long division puzzle (Reconstruct a long division given less than a quarter of the digits, and all of those are wrong) didn't last the night. So let's try to make it harder. All of the ...

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