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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9
votes
2answers
321 views

A Sudoku With A Trick

Normal Sudoku rules apply in this puzzle. This is an incredibly difficult puzzle to solve and has a very clever and ingenious trick in it. I request solvers to show their work at different stages of ...
4
votes
1answer
277 views

A slightly different type of Sudoku puzzle

The following image shows two valid Sudokus. The first was copied verbatim off Wikipedia, and the second was obtained by rotating 90 degrees. Any two distinct valid Sudokus must differ in at least ...
8
votes
2answers
189 views

Making 100 starting with two 1s

You have an empty blackboard. At each step, you can either write two ones on the blackboard, or erase two copies of a number n and replace them with n−1 and n+1. What is the fewest number of steps it ...
13
votes
3answers
898 views

A line not intersecting points in the plane

Is it possible to draw a finite or infinite set S of points in the plane, such that any line drawn in this plane neither intersects with exactly one point in S or an infinite number of points in S?
6
votes
2answers
98 views

Vertices of a regular $13$-gon and $14$-gon on a circle with center angle $< 1°$

All vertices of a regular $13$-gon and all vertices of a regular $14$-gon lie on a circle and divide it into $27$ circular arcs. Is there always an arc, which corresponding center angle is less than $...
8
votes
0answers
156 views

What's the name of the kind of puzzle where in-story solvers have more information than us, and how far they get is a clue?

It involves logical/mathematical puzzle(s), so no wishy washy different interpretations like in riddles. The puzzle in question tells a story involving a puzzle, but some details about the puzzle in ...
16
votes
2answers
2k views

Knights and knaves in a foreign language

You die and ascend to heaven, there is a knight (truth-teller), a knave (pure liar) and a joker (random) sitting on a cloud - they all look the same. In order to gain entry you must determine their ...
15
votes
1answer
312 views

Chess A Knight's Journey

You'll need to know about: A game that has existed for over 1500 years A game that doesn't exist ♞ → I → II → III → ... Answer = Xxxxxxxxx
-1
votes
2answers
251 views

4 Talking Clams, and treasure

After going to the depths of the ocean, you have finally reached it: the ultimate treasure of the world. However, when you go inside the sacred treasure room, you are presented with the Four Clams. ...
3
votes
3answers
793 views

4 Doors and a Half Value prize

You're on a game show, playing for 1 million dollars! You've made it to the final round, there are 4 doors, you pick a random door (obviously, there's a 1/4 chance for all of them, let's say you ...
23
votes
3answers
3k views

3 Numbers on Hats, A = B + C

This feels like it should be a common puzzle, but I haven't found anything exactly like it searching online, so here goes. Apologies if it's a duplicate. Three logicians, person 1, 2, and 3, along ...
5
votes
2answers
258 views

Even and odd game variant

You are playing a game with your friend on a $7$x$7$ grid board. In every turn, you begin by putting a $0$ (zero) on any empty square on the board, and then your friend puts a $1$ (one) on a different ...
5
votes
6answers
505 views

Good resource for daily Sudoku Puzzles [closed]

I love solving puzzles, It keeps my brain active. Previously I used to solve newspaper "Sudoku" which were fairly easy. Then I solved some interesting puzzles in the book below. Mastering ...
3
votes
1answer
216 views

100 Prisoners and 3-state clock

100 Prisoners and a clock seems far too easy on the prisoners, so the exact same question, except that they must change the clock by exactly 4 hours: There are 100 prisoners who are given a chance at ...
31
votes
10answers
7k views

100 Prisoners and a clock

There are 100 prisoners who are given a chance at freedom. The prisoners are randomly picked to visit a room where there is only a nonfunctional wall clock with a knob for manually changing the time. ...
2
votes
2answers
295 views

Four Mathematicians, Four Poker Hands and Four Clues

These four mathematician friends play poker every Saturday night. They always have a twist for the very last hand, just for fun. This Saturday the twist was “Factorial Clues”. The rule for the last ...
1
vote
1answer
248 views

Her granddaughter is the only daughter of my brother

Pointing to a woman, Abhijit said, "Her granddaughter is the only daughter of my brother." How is the woman related to Abhijit? Sister Grandmother Mother-in-law Mother Source of the ...
1
vote
1answer
141 views

Adding up divisors of integers

Alice and Bob play a game, taking turns. Alice starts and writes an integer between 1 to 10 on a blackboard. Then Bob adds any integer between 1 to 10 to this number and writes it on the blackboard. ...
13
votes
4answers
7k views

Who is the thief? An elementary school teacher had her purse stolen

This puzzle is not mine, but I couldn't find an original source. I edited it somewhat. An elementary school teacher had her purse stolen. The thief had to be Sammy, Karin, Arnold, Harry, or Liza. ...
3
votes
4answers
565 views

Find two numbers based on either their multiplication or exponent

There are two mathematicians with incredibly strong memories sitting in a coffee shop passing the time. Their server proposes a game: First, he gives them a large number: $2176782336$ Then he ...
5
votes
1answer
301 views

Nurikolor (Level 1)

Next level: Nurikolor (Level 2) Welcome to my new puzzle: the NURIKOLOR, which is essentially the colored version of Nurikabe, but not exactly, with a few twists. The rules are simple: There are ...
13
votes
4answers
37k 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 ...
8
votes
1answer
1k views

Is there another name for this puzzle? (Kyudoku, Nine Find)

Is there another name for this type of puzzle? I can only find two examples of it online: https://www.brainzilla.com/logic/kyudoku/ http://ninefind.com/ In the game you start with a 6x6 grid filled ...
6
votes
0answers
201 views

Trying to find a 2020 puzzle hunt with a puzzle based on Among Us

I am trying to find a puzzle hunt that I believe was held in 2020. It contained a puzzle based on the game Among Us with 26 characters, and you had to decide who were the imposters. The imposters all ...
20
votes
3answers
2k views

Making a 9 digit number divisible by 11

Alice and Bob play the following game, taking turns. Alice starts and writes a non-zero single digit number at the blackboard. At every turn, each player adds a single digit at the right of the ...
3
votes
5answers
799 views

Can you fill the cells by integers? [duplicate]

Can you fill the cells with integers so that all the equalities must be true?
14
votes
1answer
693 views

Up like a rocket ship

This is a Palisade (or 6 Cells) puzzle. The rules are: Thicken some of the pentagons' sides so the thick borders outline regions of six pentagons apiece. Any pentagon with a number in it indicates ...
12
votes
2answers
921 views

Making a 10 digit number divisible by 3

Alice and Bob play the following game, taking turns. Alice starts and writes a single digit from 0 to 9 at the blackboard. At every turn, each player adds a single digit at the right of the current ...
-4
votes
1answer
151 views

After walking 6 km, I turned to the right and then walked 2 km [closed]

After walking 6 km, I turned to the right and then walked 2 km. After then I turned to the left and walked 10 km. In the end, I was moving towards the North. From which direction did I start my ...
8
votes
3answers
460 views

Which Demon Spoke?

While wandering, you encounter a pond, in which two demons are bathing. One is labelled 'honest', meaning they always tell the truth, and the other is labelled 'liar', which means they always lie. As ...
23
votes
4answers
3k views

On which day The Joker usually going on a date?

You are an investigator. You are to investigate The Joker to know on which day he usually goes on a date with Harley Quinn. The Inspector said that The Joker is lying if and only if it's Monday, ...
-2
votes
7answers
18k views

2x2 row and column equations

Rules: No paper or notes, but a calculator is accepted. Post the exact time min wise of how long it took. And obviously give the answer.
16
votes
1answer
311 views

A Dotless Kropki

Rules of Kropki: Each row and column contains one occurrence of each digit from one to the size of the grid. All pairs of orthogonally adjacent cells containing numbers with a 1:2 ratio are marked ...
6
votes
1answer
369 views

How to solve this Loopy puzzle efficiently with little backtracking?

I would like to solve this Loopy (Cairo) puzzle: But I would like to do so with as little backtracking as possible. By this I mean that I want to have at most one pending guess at a time; I do not ...
-1
votes
2answers
240 views

Filling up squares! ⬜ ⬛ [closed]

You have a white grid of size a) 9x9 b) 10x10 and you are asked to paint some squares black. Your generous friend has given you a challenge: Can you paint them so that each white square has only one ...
8
votes
2answers
994 views

Coloring positive integers 'black or white'

Each of the positive integers from 1 to n is colored either black or white. You can repeatedly choose a number m and recolor m together with those numbers, which are not coprime to m. At the beginning ...
0
votes
5answers
157 views

Mastermind puzzle: 3548 has 2 correct, one in right place [closed]

Hints: 3548 - 2 correct digits, but only 1 in the right place 4860 - 1 correct digit, but in the wrong place 2356 - 3 correct digits, but only 1 in the right place 2584 - 2 correct digits and in their ...
3
votes
2answers
204 views

3 hats with numbers, where 2 hats sum to the third

I have outlined a puzzle below, and provided two sources which provide answers. I am disputing that the answer provided in the sources is correct, and I am looking for others to validate or invalidate ...
10
votes
2answers
720 views

Can you solve this Masyu puzzle?

Hey guys, enjoy this Masyu puzzle! For those unfamiliar with Masyu, here are some instructions: The goal of Masyu is to connect the circles on the grid via a line that closes itself and also does not ...
11
votes
1answer
223 views

Stostone - Aoi's Big Birthday

Rules of Stostone: Shade exactly one stone, an orthogonally-connected group of cells, in each region. No two stones in different regions are adjacent. If a number is in a region, it tells the size of ...
20
votes
2answers
1k views

Beans under the chessboard

Under every grid cell of a chessboard, I put either one bean or nothing. Now if you choose a (grid) rectangular area on the chessboard, then I will tell you the parity of the number of beans under ...
11
votes
2answers
506 views

Mosaic by Albrecht Dürer

This is a visual puzzle (known as "mosaic" or "fill-a-pix") with the same rules as MineSweeper: The grid is to be filled with colored and white tessera. Choose whatever color you like for the colored ...
3
votes
1answer
183 views

Quadruped Mosaic

This is a visual puzzle (known as "mosaic" or "fill-a-pix") with the same rules as MineSweeper: This puzzle has exactly 100 x 100 cells. The grid is to be filled with colored and ...
-2
votes
0answers
72 views

Connect the Balls [duplicate]

Draw only 4 lines join all the 9 balls. Hint- Bonus Question- Question Source
4
votes
2answers
279 views

Why are 2s not possible in these Sudoku cells?

I recently was playing Sudoku on my iPad. As I was stuck on the puzzle I clicked on "Tip" to receive a hint on how I can solve this Sudoku (I am still learning the game) - so please don't ...
1
vote
1answer
425 views

Knight or Knave

On the island of knights and knaves (where knights always tell the truth and knaves lie), you meet two islanders named Penny and Quinru. Penny: Both Quinru and I are knaves! Who is a knight and who ...
66
votes
18answers
24k views

Are there eighteen or twenty bars in my castle?

Two friends, Mark and Rose, are very famous logicians; they are so clever that they can deduce any logic connection possible in a matter of minutes even from the most vague situation. Unfortunately, ...
4
votes
2answers
2k views

Are there any sudoku puzzles combined with magic squares? [duplicate]

As everyone knows, in Sudoku the sum of each row and column is 45. So all Sudoku solutions are some kind of magic square. My question is: Has anyone seen a Sudoku puzzle combined with the magic square ...
7
votes
1answer
842 views

What is the fewest number of clues on a rotationally symmetrical sudoku grid with a unique solution?

It is known that the minimum number of clues a sudoku must have to have a unique solution is 17. But on every website I've seen for them, I haven't found any that are rotationally symmetrical. I once ...
31
votes
13answers
21k views

Protagoras's Paradox. An Unsolved Court Case

Many years ago, a Law teacher came across a student who was willing to learn but was unable to pay the fees.The student struck a deal saying, "I will pay your fee the day I win my first case in the ...

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