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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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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 ...
Bob Bixler's user avatar
0 votes
1 answer
71 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. ...
Will.Octagon.Gibson's user avatar
7 votes
1 answer
359 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 ...
Xavier Castillo's user avatar
3 votes
3 answers
542 views

Knights, Knaves, and Spies

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 ...
user91410's user avatar
4 votes
1 answer
280 views

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

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 ...
Rahul Krishna's user avatar
-1 votes
0 answers
102 views

Brooklyn Nine-Nine: Holt’s Season 2 Puzzle [closed]

I’ve seen several answers to the Weighing Islanders puzzle Captain Holt poses to the squad in Season 2, but I had a different train of thought when solving it. Did anyone use the process of ...
Allie Zuniga's user avatar
2 votes
1 answer
189 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 ...
Liam Stygian's user avatar
10 votes
2 answers
567 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 ...
Will.Octagon.Gibson's user avatar
4 votes
3 answers
818 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. ...
Will.Octagon.Gibson's user avatar
29 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 & @...
Will.Octagon.Gibson's user avatar
14 votes
3 answers
799 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 ...
Will.Octagon.Gibson's user avatar
1 vote
1 answer
143 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/...
Thirdy Yabata's user avatar
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 ...
Renee Romero's user avatar
7 votes
1 answer
161 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 ...
Xavier Castillo's user avatar
15 votes
1 answer
687 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 ...
Jafe's user avatar
  • 78.8k
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 ...
Thirdy Yabata's user avatar
-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 ...
Nick's user avatar
  • 1,701
2 votes
1 answer
237 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
William's user avatar
  • 29
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 =?
alex's user avatar
  • 29
6 votes
1 answer
571 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" ...
TheLittlePeace's user avatar
8 votes
1 answer
634 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 ...
Xavier Castillo's user avatar
2 votes
2 answers
217 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 ...
Cristof012's user avatar
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 ...
Bob Bixler's user avatar
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. ...
Presh's user avatar
  • 643
1 vote
5 answers
572 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 ...
Hemant Agarwal's user avatar
3 votes
1 answer
173 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 ...
Josh's user avatar
  • 173
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.
Jujustum's user avatar
  • 4,232
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 ...
Bubbler's user avatar
  • 16.3k
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 ...
Josh's user avatar
  • 173
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 (...
Jafe's user avatar
  • 78.8k
3 votes
1 answer
328 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 ...
Shivam's user avatar
  • 153
9 votes
3 answers
375 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. ...
Angel Sachse's user avatar
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 ...
3-1-4-One-Five's user avatar
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 ...
tkf's user avatar
  • 457
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 ...
Paul Kolk's user avatar
  • 270
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 ...
user23087's user avatar
  • 912
9 votes
1 answer
237 views

Reconstruct a long division given less than a quarter of the digits, and all of those are wrong

Inspired by "The Puffin Book of Brainteasers" I decided to try my hand at creating a long division missing digits problem where all of the displayed digits are wrong. On searching I found ...
user23087's user avatar
  • 912
9 votes
1 answer
286 views

Communicate square on a 3-by-3 grid by flipping precisely one of 13 coins

A coin is placed on each of the $13$ squares in the following diagram: Each coin may be showing heads or tails arbitrarily. An adversary points to a square in the $3\times 3$ grid. You must ...
tkf's user avatar
  • 457
2 votes
1 answer
202 views

A Framework puzzle

About Framework puzzles: A Framework puzzle is similar to a Fill-in puzzle, except there is no rigid crossword-style grid, the tradeoff here being that you get fewer hints for placing (in this case) ...
CrSb0001's user avatar
  • 2,423
20 votes
2 answers
734 views

Torus Flow Free

Rules: this is a flow free warp puzzle with a 9x9 grid. connect the respective letters together with lines that travel orthogonally through the centers of grid cells. additionally, the sides of the ...
Omega_3301's user avatar
10 votes
1 answer
336 views

3-clue 5x5 Hidato

Rules Fill the grid with numbers 1-25 such that consecutive numbers are adjacent orthogonally or diagonally Try solving it in Penpa There are only about a dozen 5x5 Hidatos with only 3 clues. (...
Tom Sirgedas's user avatar
  • 1,728
1 vote
2 answers
220 views

Solve the Alphametic: SOUNDS / WOW = ELK

This is a long-division problem in which letters are substituted for numbers. Solve the problem. Determine the number value of each letter; and when the letters in each one have been arranged in order ...
William Bibb's user avatar
12 votes
1 answer
668 views

Bare Bones – a semi-DIY crossword

This is part 64 of the puzzle series Around the World in Many Days. Each part is solvable on its own. Dear Puzzling, This is a semi-DIY crossword. Shade some cells in the grid so that the grid has ...
Jafe's user avatar
  • 78.8k
11 votes
2 answers
1k views

New record for minimally clued 7x7 Hidato (now with 6 clues!)

Rule of Hidato: Fill the grid with consecutive numbers such that they connect orthogonally and diagonally. Solve the following three Hidato puzzles. 8 clues 7 clues 6 clues You can solve these on ...
Bubbler's user avatar
  • 16.3k
5 votes
1 answer
182 views

Current record for minimally clued 7x7 Hidato (16 clues)

Background Back in March, I posted this question on the Puzzling Stack Exchange asking how many clues were needed to create a 4x4 Hidato puzzle with a unique solution. Sometime after this, I took a ...
CrSb0001's user avatar
  • 2,423
11 votes
2 answers
2k views

How many Friends are there in the circle?

On the island of Friends and Foes, every citizen is either a Friend (who always tells the truth) or a Foe (who always lies). Seven citizens are sitting in a circle. Each declares “I am sitting between ...
Will.Octagon.Gibson's user avatar
2 votes
1 answer
133 views

Memorial Day puzzle

In 2025, Memorial Day will be on May 26. Also, in 2026, Memorial Day will be on May 25. Notice that the last two digits of the year and the Memorial Day date in May have just switched places. The same ...
Geoffrey Trang's user avatar
-2 votes
2 answers
226 views

Flipping DIP switches

About 30 years ago, I bought a memory extension card. At first, I was hesitating: there were 8 dip switches and no manual. Then the owner recalled that 4 switches indicated the memory on the ...
kaksi's user avatar
  • 429
7 votes
1 answer
421 views

Off-duty guards on liar island

It's a little-known fact that the guards on Liar Island have to continue their slavish devotion to the individual rules dictating the veracity of their statements. Of course, some always lie, and some ...
Dr Xorile's user avatar
  • 23.7k
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 ...
Sny's user avatar
  • 3,185

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