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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-2
votes
1answer
72 views

Variant of blue eyes puzzle

There are a total of 200 players assigned to either A or B at a certain venue. There are actually 100 of each, but the players don't know that. They don't know which one they are. Of course, there is ...
1
vote
1answer
92 views

Organs of the Enterpeton

An enterpeton has arrived at the bathhouse. Enterpetons are strange reptiles with exposed organs. Four of these organs can answer questions, and follow certain rules. These organs are: the heart, ...
12
votes
2answers
295 views

Encrypted Pentopia

Rules of Pentopia: Place some pentominoes into the grid (not necessarily all of them) so that they do not touch each other, not even diagonally. Pentominoes cannot repeat in the grid; rotations and ...
0
votes
1answer
131 views

The Primordial Ones

The bathhouse you work at is being visited by some of the primordial beings from the pools of chaos. You have been tasked with finding out which pools they came from, so that the proper form of chaos ...
3
votes
0answers
118 views

Mega-puzzle of many number puzzles: Nikoli Octathlon

This puzzle has been my Moby Dick of puzzles for so long. It's from MellowMelon's old puzzle site and is a Nikoli-based megapuzzle with eight sub-puzzles. I'm copying the puzzle image from there so as ...
0
votes
2answers
118 views

The Rainbow Serpents

At your bathhouse job, you encounter a pair of rainbow serpents, each having two heads, hiding behind a wide pillar. They seem to be bent around the pillar with a head from each serpent visible on ...
2
votes
1answer
167 views

Which plume is which?

One day, at the spirits' bathhouse you work at, you encounter 5 dragons, who have decided to share a bath. Due to the lighting you can only see what is above the water, that being 5 tails, and 4 heads ...
4
votes
1answer
161 views

Mastermind: What should I guess next? That depends

Bob was playing a popular adventure game on his computer, and he came across a Mastermind minigame. Here's the results of his first four guesses: Bob has never been great at solving logic puzzles on ...
31
votes
7answers
2k views

Two out of a dozen cartons have Easter eggs. Two people try to find one Easter egg carton, each using a different strategy. Who is expected to win?

I have found a counter intuitive puzzle. I have read the answer given at the source and understand it completely. But, what I am unable to understand is why my intuition turned out to be wrong. ...
-2
votes
0answers
76 views

A problem from order and ranking [closed]

Rita is sitting 5th from the left end of row and Sita is 11 th to the right of Rita and Tina is 4 th to left of Sita. Madhuri is 8th to right of Tina. What is the total number of students in the row ...
25
votes
2answers
1k views

Encrypted Snake (Grid Puzzle)

Rules of Snake: Shade some cells to form a non-intersecting path which does not touch itself, not even diagonally. Black circles must lie on one end of the path. White circles must lie somewhere ...
-1
votes
1answer
308 views

The marvelous puzzling space prize

Prologue Three friends wanting to earn the marvelous puzzling space prize offered by a supercomputer, joined a competition. Here are the competition's rules they read out in the competition ...
15
votes
1answer
346 views

Sum-until-1 Fillomino: Odds, Fibonacci, and Pi

Fillomino rules (taken from Nikoli): 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 ...
1
vote
1answer
167 views

Blood relations - who is married to whom and reads which magazines?

In a family of eight persons - P, Q, R, S, T, U, V and W - there are four males and four females. There are three married couples and two persons are unmarried. Each of them reads a different magazine,...
13
votes
1answer
264 views

Sub Battle Sudoku

Please find below a variant Sudoku which incorporates elements of Star Battle. The Sudoku is a standard irregular Sudoku, and the clues outside the grid are sandwich clues: the sum of digits strictly ...
3
votes
1answer
417 views

100 blue-eyed people riddle N=4

The solution of this riddle is usually given with explicit reasoning for two cases: Case where there is only 1 blue-eyed person, Case where there are 2 blue-eyed people. That logic is clear, and I ...
8
votes
1answer
430 views

Where's the path?

A person was shading several unit squares in a square grid, to create a path from the bottom left corner to the top right corner. The path stepped from each square to the next either horizontally or ...
13
votes
1answer
259 views

Mid-loop: Coming Soon

Rules of Mid-loop: Draw a single loop passing through all of the black dots. The loop may not branch off, intersect, or move diagonally. The loop cannot bend at the black dot. Each black dots denotes ...
10
votes
2answers
424 views

Transform a pile of cards in reverse order

There are 52 cards on a table and numbered in order from 1 to 52 with number 1 on top. The following operation can be repeatedly done: split the pile into two piles without shuffling and take cards ...
10
votes
2answers
577 views

When was Ensquare born?

Professor Matlogic posed this question to his smartest math student: "Famous mathematician Ensquare was born on this day, this month and this year AD at this time (hour and minutes) pm. True to ...
10
votes
2answers
315 views

Trio Tapa: Introduction

Rules of Tapa (copied from here): Shade some cells of the grid. Shaded cells should form a single [orthogonally] connected group; no 2×2 square should be fully shaded. Some cells have clues in them. ...
14
votes
3answers
309 views

Cross ALL the Streams

This grid deduction puzzle is a hybrid of three puzzle types: Cross the Streams, Tapa and Star Battle; rules for each are summarized below. In this grid, every cell is to be shaded either red, blue, ...
3
votes
2answers
243 views

Cursed Knights and Knaves

You are packing up after a week-long stay at the Verity Inn. You came here, to Truth Town, to visit your friend but now it's time to go home. You feel in good spirits as you pack your bags. As you are ...
8
votes
2answers
897 views

Five positive integers in a row, each being the sum of the digit sum of its neighbours

Five positive integers should be put in a row such that each integer is the sum of the digit sum of its neighbours. The integers at the beginning and at the end have only one neighbour, i.e the first ...
5
votes
1answer
125 views

Sum and product of 9 digits

Adding single digits 1 to 9, the result is 45 and their product is 362880. Are there any other 9 single digits with sum 45 and product 362880?
11
votes
3answers
1k views

Find an integer where each sum of 5 consecutive digits is prime

Find the largest positive integer with the following properties: every sum of 5 neighboring digits in its decimal representation is a prime number. those prime numbers get smaller and smaller from ...
17
votes
2answers
656 views

XV Sawtooth Sudoku

Please find below a variant Sudoku puzzle, based on a combinatorics problem I was having a look at. The timing is right, as I recently saw @BeastlyGerbil back in chat, and I know that user is a big ...
10
votes
1answer
820 views

8 dice with a product being a square

8 standard six-sided dice with faces numbered 1, 2, 3, 4, 5, 6 each are thrown at the same time and the product of the dice is written down on a paper. This process is repeated until you are able to ...
3
votes
1answer
586 views

A tough Word-Nurikabe puzzle

I came up with this Word Nurikabe Puzzle, which was NOT a part of the Puzzle Ramayan, the qualifiers for Indian Puzzle Championship. Rules Place the given words in the grids ‘islands’, so ...
2
votes
2answers
203 views

How to get started on this Slitherlink (No Swiss)?

This is a puzzle from Round 4 of WPF's Puzzle Grand Prix this year. It's a Slitherlink with the additional rule that "Every Swiss cross-shaped arrangement of five cells must contain at least one ...
-3
votes
1answer
232 views

How can a liar and a truthteller prove their identities? [closed]

You come across two people. One is a liar who always lies and the other is a truthteller who always tell the truth. You don't know who is who though. Both these people are allowed to say one sentence ...
6
votes
2answers
487 views

Who won the race?

4 players enter a race. The judge is not at the finish line to judge the ending. When the judge shows up to award the prize, these are the statements by 4 players Alpha - I won the race Beta - I came ...
7
votes
1answer
229 views

Toroidal Weaved Truncated Square Tiling Tapa

Rules of Toroidal Weaved Truncated Square Tiling Tapa: The grid wraps around horizontally and vertically and also is divided into several 1-cell and 3-cells tiles. Shade some tiles such that all ...
13
votes
1answer
728 views

Transform each square of a chessboard to zero

Each square of an 8x8 chessboard is marked with a positive integer. The integers can be changed according to the following two rules: (1) all integers in a row are doubled (2) all integers in a column ...
-3
votes
1answer
121 views

Can you help to solve this triangle puzzle [closed]

Find the missing number (triangle) Please write the logic also.
1
vote
1answer
241 views

Can Arrows puzzles have multiple solutions?

I am trying to make an Arrows puzzle, but I don't know if there are multiple solutions. For those who don't know, an Arrows puzzle starts with a grid of numbers (example from SE) surrounded by empty ...
3
votes
1answer
677 views

What's the next step for this Kakuro puzzle?

What's the next step for the below Kakuro puzzle? Source: Puzzle Page app
-4
votes
1answer
151 views

Who Counted More?

Two persons, one standing at the door of his house and the other walking up and down the pavement, were counting passers-by for a whole hour. Who counted more? Source: - From here.
31
votes
2answers
3k views

The Second Hardest Logic Puzzle in the World

This puzzle is an original creation of mine (as far as I know), although other people have solved it before me. You meet five people: Alice, Bob, Carol, Daniel and Evie. Your aim is to ask yes/no ...
10
votes
1answer
174 views

3D Tapa - Count to Five

Rules of 3D Tapa: The grid is a 3-dimensional cubes, represented here by layers of cubes from top to bottom. Shade some cubes such that all shaded cubes form a single orthogonally (in 3-axis) ...
15
votes
2answers
535 views

A maze of placed faces

Twenty-nine images of famous people have been specifically selected and carefully placed so as to form a maze (below). However, two of the images - both of US Presidents - have been redacted (marked '...
5
votes
1answer
468 views

The next steps for this Kakuro puzzle

What are the next steps for this Kakuro? I've solved most of it, but there is an area I'm stuck on. Source: Puzzle Page app
13
votes
5answers
2k views

Safecracking Puzzle

There is a combination safe with four switches on the front, each with three positions (low, medium, and high). If the switches are set into an opening combination, then when you try to open the safe, ...
7
votes
1answer
306 views

“Puzzle Waffle”

A black man, tilting his head in satisfaction and checking it was about lunchtime, entered the Sphinx Café in downtown Washington D.C. on a Friday out of boredom with his usual lunch haunt and greeted ...
8
votes
2answers
462 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 ...
7
votes
2answers
122 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 $...
13
votes
3answers
982 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?
11
votes
0answers
182 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
292 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
259 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 ...

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