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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10
votes
4answers
254 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?
8
votes
0answers
139 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 ...
5
votes
2answers
254 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 ...
3
votes
1answer
210 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 ...
1
vote
1answer
138 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. ...
6
votes
0answers
197 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 ...
14
votes
1answer
691 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 ...
-4
votes
1answer
147 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
457 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 ...
12
votes
2answers
916 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 ...
16
votes
1answer
309 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 ...
-1
votes
2answers
238 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 ...
3
votes
5answers
797 views

Can you fill the cells by integers? [duplicate]

Can you fill the cells with integers so that all the equalities must be true?
8
votes
2answers
990 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 ...
1
vote
5answers
145 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
203 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 ...
11
votes
1answer
222 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 ...
7
votes
1answer
134 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 ...
-2
votes
0answers
72 views

Connect the Balls [duplicate]

Draw only 4 lines join all the 9 balls. Hint- Bonus Question- Question Source
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
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 ...
1
vote
1answer
423 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 ...
1
vote
1answer
247 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 ...
15
votes
1answer
309 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
vote
1answer
84 views

Finding a lock combination [closed]

Here is a puzzle that I recently encountered: You have a four digit lock with the following clues. When you enter 1378, one digit is correct and well-placed. When you enter 2834, nothing is correct. ...
18
votes
1answer
544 views

Slitherknot (Double Slitherlink)

This is a variation on the classic Slitherlink Puzzle. However, instead of creating one loop, you must create 2 separate loops. The two loops can not share any edges, however they can cross or meet on ...
-6
votes
1answer
108 views

How is the boy related to the girl? [closed]

Pointing to a boy a girl said "He is the son of the daughter of the father of my only uncle. "How is the boy related to the girl?" A standard yet simple technique will be highly ...
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
4answers
2k views

Who is the liar (Number of liars)?

There are 5 people. Each one can be lying or telling the truth, and they can't switch. Below, each person tells us how many liars exist in the group. There are at least 3 liars. There are at least 2 ...
2
votes
2answers
294 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 ...
8
votes
1answer
209 views

Gaps - Square Numbers

Rules of Gaps: Fill some cells with stars, so that each row and column contains exactly two stars. The stars cannot touch each other, not even diagonally. Numbers outside the grid indicate the number ...
-1
votes
1answer
96 views

What replaces the question mark in the blood relation problem? [closed]

If A + B means A is the father of B If A × B means A is the sister of B If A $ B means A is the wife of B If A % B means A is the mother of B If A ÷ B means A is the son of B What should come in place ...
-2
votes
1answer
140 views

A Blood Relation problem [closed]

In a family there are two married couples, two daughters, three sons and two brothers. Rohan is the son of Soni who is the daughter of Rajeev and wife of Lucky. Riya is the grand daughter of Rajeev. ...
1
vote
3answers
601 views

Blood relation problem - how is G related to S? [closed]

A is the son of P and brother in law of T, who is the sister of G. B is the husband of K. K has only two children, T is one of them. S is the mother of A and sister of W who is the husband of R. U is ...
13
votes
1answer
874 views

A walk after dark

This is a Palisade (or n-Cells) puzzle. The rules are: Thicken some of the squares' sides so the thick borders outline cells. One such cell comprises just one square; one cell comprises precisely two ...
3
votes
2answers
163 views

On which date was Marina born?

The puzzle is as follows: In 2012, which began on a Sunday, Marina was happy because her birthday was on a Saturday and she celebrated it with her friends. We know, Marina was born in a year where ...
8
votes
3answers
296 views

Toroidal Pipes Puzzle: T's and Bulbs Only

A continuation in the Pipes puzzle series. Problem statement for math nerds: Let $G(N)$ denote the graph consisting of cardinally adjacently linked lattice points on an $N \times N$ toroidal grid. For ...
15
votes
1answer
1k views

When you stop at the top of a Ferris wheel

This is a Palisade (or Ten-Cells) puzzle. The rules are: Thicken some of the squares' sides so the thick borders outline cells of ten squares apiece. Any square with a number in it indicates how many ...
7
votes
3answers
418 views

Can you find and capture a shapeshifter?

A town was invaded by aliens, and some of its residents were kidnapped and replaced by shapeshifters. You're tasked with capturing one of the shapeshifters. Here's the setup: There are 7 residents of ...
13
votes
1answer
445 views

Windmill: A Masyu Puzzle

The standard Masyu rules apply.
0
votes
0answers
54 views

Grids with tiles of two colors and connectors

Make a square grid with an even side. Make a continuous trail which passes through all small squares; the trail ends where it started. Where there is an angle you can put a red or a blue tile. On ...
0
votes
1answer
79 views

How to solve the attached sudoku?

Please explain the logic. I am not trying to solve it using trial and error or using any software. I am just looking for the next step. This sudoku is from apple 'Sudoku King' app.
2
votes
1answer
158 views

How could I solve the attached Sudoku?

Please explain the logic. I am not trying to solve it using trial and error or using any software. I am just looking for the next step. This sudoku is from apple 'Sudoku King' app.
1
vote
1answer
124 views

What is the greatest number of pencils that you cannot buy? [duplicate]

A shop sells pencils in boxes of 31 and 38. What’s the highest number of pencils a person cannot buy? In general, if the shop is selling pencils in boxes of p and q, then what is the highest number ...
10
votes
1answer
973 views

My grandfather's coins

When my grandfather died, he left his fine collection of coins, not more than 2500 of them, to his children, a different number to each of them, and in decreasing amounts according to their ages. To ...
12
votes
1answer
262 views

9x9 Sudoku Slitherlink Hybrid

I previously created a combined slitherlink and sukoku puzzle, but I was unsatisfied because the grid was smaller then a regular sudoku. So I made another, larger one. Below is a 9 by 9 grid. This is ...
13
votes
3answers
2k views

What is the age of the old man?

In autumn of the year 2003 an old man was asked about his age. He answered: "I was born on a Sunday morning in summer and I celebrated my seventh birthday on a Sunday morning too!" How old ...
9
votes
1answer
147 views

Sudoku: Episode 64 - Attack of the Clones

An 8x8 Sudoku where you technically only have to figure out 32 cells! Twice Half the cells, double the clues! Penpa Link Rules Normal Sudoku rules apply. Values are 1-8. Boxes are the 4x2 regions ...
17
votes
2answers
578 views

Pipes Puzzle Uniqueness

In the puzzle game Pipes, a space-filling tree of pipes (which may have either one, two, or three neighboring connections each, but not four) is scrambled by a series of tile rotations, and the goal ...
1
vote
2answers
171 views

To Mock a Mockingbird: 4 brothers

On page 30 of Raymond Smullyan's book To Mock a Mockingbird, we are told that there are four brothers, indistinguishable in appearance, of which Arthur is an accurate truth-teller, Bernard is an ...

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