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Questions tagged [logical-deduction]

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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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Found this weird cave with a prime spade right in the center... but it seems impossible? Oh, apparently, I need to use the set of tetrominoes lying nearby. Penpa link Rules This is a Cave puzzle. ...
bobble's user avatar
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14 votes
1 answer
573 views

The priests of a certain order do not use the words "yes" and "no". Instead, they say "qui", "quae", and "quod". That's right. Three words, each of ...
fblundun's user avatar
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-7 votes
0 answers
83 views

Is it possible to place exactly one positive integer in each shape such that the following conditions hold? Only the number $1$ is repeated. Each dodecagon's number is the product of the numbers in ...
designer's user avatar
  • 1
15 votes
8 answers
2k views

Can a 10 * 10 square be paved with 1*4 rectangular stone plates? I seek a very intuitive and simple answer to this puzzle. P.S. Will post the source later. The source contains the answer but it is not ...
Hemant Agarwal's user avatar
  • 7,845
2 votes
1 answer
197 views

Puzzle #9 in A Most Puzzling Murder Mystery by Bianca Marais: After midnight, five women sneak from the castle’s foyer to head out for various nefarious reasons. Each of them has a specific ...
Des Brown's user avatar
  • 51
-1 votes
0 answers
215 views

I am developing a game that generates puzzles every day (https://125034.pages.dev/). It's my opinion that these puzzles are like Einstein's Riddle in 1D. The game and I have created four "v=0&...
a life's user avatar
  • 304
5 votes
0 answers
181 views

I’ve made a small browser puzzle called Codextri where you have to identify a hidden set of three letters by guessing words. Each guess returns a score based on how many of those hidden letters your ...
Celestialien's user avatar
  • 51
0 votes
1 answer
112 views

Rules to fill out the grid: I must use 3 of each symbol in each row, and in each column. I cannot use 3 consecutive identical symbols (horizontally or vertically). A solid border indicates that the ...
Improve's user avatar
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15 votes
5 answers
2k views

Here is (yet another) prisoner riddle. I made it up (maybe it was asked before, but to the best of my knowledge I'm the first to ask it - correct me if I'm wrong). There are 1000 prisoners who are ...
Dean Kraizberg's user avatar
  • 323
1 vote
1 answer
229 views

This is a lightweight puzzle, hopefully entertaining but not difficult. Since my FIDE rating for classical Chess is 2343 at the time of writing, I recommend you do not post a solution to this puzzle ...
happystar's user avatar
  • 7,920
2 votes
4 answers
344 views

LinkedIn's Queen #564 (HARD difficulty) I am watching the commentary of today's Queen puzzle (a 1* Star Battle puzzle), given that I complete it in about 2 minutes. But one thing I don't quite ...
Hector Lai's user avatar
  • 109
-3 votes
1 answer
262 views

Here's a famous Lewis Carroll problem: Babies are illogical Nobody is despised who can manage a crocodile Illogical persons are despised The conclusion is: Babies cannot manage crocodiles. I've ...
Bob Bixler's user avatar
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8 votes
4 answers
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1/2024 is equal to $0.000\overline{a9407114b245059c88d375}$. Can you find the values of a, b, c, and d without using a calculator? Long division is trivial. Can you use other ways to find the missing ...
Thirdy Yabata's user avatar
  • 1,969
0 votes
1 answer
171 views

Puzzle You are on an island inhabited by three types of people: those who only tell the truth (knights), those who only tell lies (knaves), and those who sometimes tell the truth and sometimes tell ...
Mr Frog's user avatar
  • 111
1 vote
1 answer
478 views

I’ve been working on the following Nonogram and got stuck partway through. I’d like to continue logically rather than by guessing, but I’m not sure what the next forced step is. Here is my current ...
Taran's user avatar
  • 19
2 votes
1 answer
190 views

The last number of months I have been reading about numerous ways on how to solve Sudokus. So far I am familiar with obvious and hidden singles, obvious, hidden and pointing pairs, obvious, hidden and ...
Anonymous196's user avatar
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0 votes
1 answer
183 views

For part C of the this problem: The Big Cube and Squares Puzzle, the solution states: However, 6 is not achieveable, because we can show by contradiction that there must be at least one 'move' that ...
Ash's user avatar
  • 3
8 votes
3 answers
868 views

To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not post an answer until 48 hours after this question is posted. Thank you! ...
Will.Octagon.Gibson's user avatar
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5 votes
1 answer
230 views

Preamble The late Dr. Bailey had a world class art collection. As stipulated in her will, 6 of her most prized positions were to be put up for auction between 6 companies and art collection groups ...
Truej's user avatar
  • 1,117
2 votes
1 answer
138 views

In designing logical puzzles (example: grid-based deduction puzzles), difficulty can come from either logical dependencies or from search space. Is there a formal way to distinguish or measure these ...
Anushka_Grace's user avatar
  • 131
6 votes
0 answers
194 views

Some background first. The gimmick for this puzzle was inspired by a recent puzzle in a mathematics discord. As part of solving that problem I learned how to use a SAT Solver to generate cases. During ...
OmnipotentEntity's user avatar
  • 351
4 votes
2 answers
875 views

I thought of a little puzzle while contemplating the Sleeping Beauty problem. The puzzle: create a variant of the Sleeping Beauty experiment (which involves one fair coin toss) where there is a ...
Tyler Seacrest's user avatar
  • 11k
7 votes
2 answers
536 views

In the following Slitherlink, where you need to make one unbroken loop over the grid with the number in each cell matching the number of edges around that cell, I noticed that the 3-2-2-1 2x2 box at ...
justhalf's user avatar
  • 6,726
12 votes
2 answers
603 views

Place a nonzero digit into some of the white cells of the grid. Shaded cells must remain blank. No digit can repeat in a row or column. In each row, the sum of the digits must be equal to some fixed ...
Bayesian Hat's user avatar
  • 341
9 votes
1 answer
517 views

This is another Minesweeper puzzle in a series I've created. I am the author of this puzzle. I wrote the code that creates it, and as far as I can tell it is my own invention, obviously based on the ...
Truej's user avatar
  • 1,117
5 votes
1 answer
372 views

This is my first post to puzzling stack exchange, please let me know of any feedback you have. It's an original puzzle I made myself. The Puzzle: Alice and Bob are in prison for life for convincing ...
Waterbottle3939's user avatar
  • 53
6 votes
1 answer
261 views

Fill each empty square with a number so that every row, every column and every irregularly shaped region contains all the numbers 1, 2, 3, 4 and 5 each exactly once. If you enjoyed this puzzle, you ...
Will.Octagon.Gibson's user avatar
  • 32.3k
4 votes
1 answer
262 views

English translation: Question 1: Which question has the same answer as this one? ( ) A. Question 8 B. Question 4 C. Question 2 D. Question 6 Question 2: Which question has a different answer from ...
Poor's user avatar
  • 67
5 votes
1 answer
225 views

The Minesweeper Puzzle nobody was asking for is back! Rules: All standard Minesweeper rules apply. All cells with a clue of 0, 1, 5, 6, 7, and 8 are revealed All possible Gray flags are revealed. ...
Truej's user avatar
  • 1,117
7 votes
3 answers
770 views

Given a line and two points A and B, which point P on the line forms the largest angle APB? Bonus question: How should we select P so that the angle APB is as small as it can be? P.S. I tried solving ...
Hemant Agarwal's user avatar
  • 7,845
5 votes
1 answer
372 views

Rules of Yin-Yang: Fill each empty cell with either a black circle or a white circle. All white circles should be orthogonally connected, so do all black circles. There may not be any 2x2 cell region ...
Mil's user avatar
  • 151
5 votes
1 answer
313 views

In Slitherlink, you are supposed to make one single loop over the edges of the grid, while each cell has a specified number of edges which are part of the loop. If there is no number then it is free. ...
justhalf's user avatar
  • 6,726
4 votes
1 answer
379 views

very much inspired by excellent What percentage of the town drinks liquor? In a certain town, 90 percent of the residents drink coffee, 80 percent drink tea, 70 percent drink whiskey, and 60 percent ...
FirstName LastName's user avatar
  • 3,026
20 votes
6 answers
3k views

In a certain town, 90 percent of the residents drink coffee, 80 percent drink tea, 70 percent drink whiskey, and 60 percent drink gin. No one drinks all four. What percent of the residents drink ...
Hemant Agarwal's user avatar
  • 7,845
4 votes
4 answers
477 views

The Ruritanian prime minister is in a fix. Thanks to a series of incompetent policy decisions, all five of her senior ministers need to be axed from their posts. However, the PM cannot afford to sack ...
Hemant Agarwal's user avatar
  • 7,845
0 votes
2 answers
402 views

Am I right that nothing can be done here?
oleedd's user avatar
  • 321
8 votes
3 answers
717 views

Arun and Disha played several games of table tennis. At five different points during the day, Arun calculated the percentage of the games played so far that he had won. The results of these ...
Hemant Agarwal's user avatar
  • 7,845
3 votes
2 answers
352 views

What next (for a new line) if without backtracking? I am more interested in moves which allow to continue solving. It looks like diagonal deductions are exhausted. A link to it for interactive play. ...
oleedd's user avatar
  • 321
0 votes
3 answers
206 views

What next? It looks like I need more techniques to avoid backtracking there. It is the hardest standard grid preset. A link to it for interactive play. Rules: Form a single closed loop out of the ...
oleedd's user avatar
  • 321
6 votes
3 answers
305 views

Seven Gods Problem: How do I identify each god's identity with the fewest questions? Description of the Seven Gods Problem: The Truth God always tells the truth. The False God always lies. The ...
王九同's user avatar
  • 71
7 votes
4 answers
982 views

What next? It is the max difficulty. I set small because it is better for learning and if you can solve small, you can solve big. I don't exclude unlikely ways and don't try most probable ways. I use ...
oleedd's user avatar
  • 321
10 votes
2 answers
532 views

Standard bingo rules apply. The solution exists and is unique. The 'correct' answer has at least a row, column or diagonal all checked. Transcription; ignore the table's empty header row. Some typos ...
Sunny's user avatar
  • 4,606
1 vote
3 answers
352 views

It is only Hard (2/4), but I'm stuck here and need help. How to find a next tower? Any is useful for learning and suitable for answering, but I need a tower which allows to continue solving of course....
oleedd's user avatar
  • 321
3 votes
3 answers
294 views

The other day, I went to a sauna and noticed the classic sand timer on the wall. If you enter when all the sand has run through (t2), you simply flip the timer and enjoy your session until the sand ...
alvi's user avatar
  • 716
1 vote
0 answers
185 views

The diamond-shaped Light Out game refers to a Light Out variant with a diamond-shaped grid, characterized by the following structural properties: Total number of rows/columns: $2k+1$ rows (where k is ...
DSTBP's user avatar
  • 183
2 votes
2 answers
451 views

This is a Towers puzzle from the Simon Tatham Portable Puzzle Collection. (Also called "Skyscrapers" elsewhere.) What's a next logical step for a next tower? I dislike guessing/backtracking,...
oleedd's user avatar
  • 321
-3 votes
2 answers
270 views

One hundred doors, three guards. Only one door leads to the truth; the others lead to false paths. The three guards are seated at a table. You do not know who is who. Their roles are as follows: – ...
boks's user avatar
  • 15
5 votes
2 answers
717 views

What is a next logical step? (For a new tower.) Brute force or guessing is not suitable because that's not how solving works. It is from Simon Tatham's Portable Puzzle Collection. The difficulty is ...
oleedd's user avatar
  • 321
6 votes
1 answer
312 views

A unique puzzle for analytical minds. Do you dare to solve it? Rules: Fill the grid with all two-digit numbers (from 00 to 99), with no repetitions. In each row and each column, no two numbers may ...
Xavier Castillo's user avatar
  • 2,536
11 votes
2 answers
1k views

A Logician has 4 students. He decides to test them. He writes a number on a piece of paper and folds it. He says: “Listen. I have written a 2 digit positive integer on this paper and Raj, Ken and Amy ...
RogerA's user avatar
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