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).
3,182
questions
27
votes
3
answers
4k
views
If A cents can be paid with B coins then prove that B dollars can be paid with A coins
Looking for an intuitive solution to the following problem:
In a certain country the following coins are in circulation: 1 cent, 2 cents, 5 cents, 10 cents, 20 cents, 50 cents, and 1 dollar. It is ...
- 2,818
7
votes
0
answers
147
views
Logic and geometry problem 2
My question is whether or not a deadlock can occur in Crisscross. A deadlock is defined as a position, an arrangement of checkers, in which the board has been filled but neither player has won.
...
- 331
22
votes
1
answer
982
views
The Metaslitherlink
This puzzle is part of the Monthly Topic Challenge #13: Variety Slitherlinks.
Below is a grid containing multiple small slitherlinks. These can be independently solved to form clues for the large ...
- 5,583
2
votes
1
answer
368
views
Sheets of paper on foreheads in a quiz show [duplicate]
I have got a puzzle that I wanted to share.
In a quiz show, three candidates were shown five slips of paper - three white and two black. Then they were blindfolded and one of the slips of paper was ...
3
votes
2
answers
348
views
Lightbulbs in Two Separate Rooms
You are in a room with six light switches. Down the hallway, there are two other rooms, each with three incandescent lightbulbs.
Each lightbulb is uniquely controlled by exactly one of the switches. ...
- 175
0
votes
0
answers
183
views
Logic puzzles: Flags and Stripes
Puzzle 1
Puzzle 2
Clues
The only instructions given to solve this is that the answer can be alpha-numeric text.
Ideas
Puzzle 1:
3 flagpoles seem to have top-balls (called a truck), while 3 don't
...
- 119
5
votes
0
answers
219
views
Shape puzzle, find the final sequesnce or word? [closed]
Clues:
The only instructions given to solve this is that the answer can be alpha-numeric text.
Ideas:
So far I have this:
SQUARE: 101111
DIAMOND: 2111112
RECTANGLE: 111211021
HEXAGON: ?1?1011
Though ...
- 119
1
vote
0
answers
184
views
Puzzle Challenge: Unraveling the the Circular Conundrum
Known are five numbers: 1, 2, 3, 4, and 5, arranged clockwise. The number after 1 is 2, after 2 is 3, after 3 is 4, after 4 is 5, and after 5 is 1. Whenever two adjacent numbers meet, it triggers a ...
- 11
7
votes
1
answer
377
views
Logic and geometry problem
My question is whether or not cycles can occur in the abstract game, Clearcut.
Clearcut
A few smart guys (and me) have been trying to either find a cycle or prove that one can't happen. Ten days ...
- 331
6
votes
1
answer
304
views
Is the Parity Sudoku solvable?
I have a new kind of grid puzzle (you could call it a variant of sudoku) I will be calling a Parity Sudoku.
Parity Sudoku is played on a 6x6 grid of integer cells with numbers ranging from 1 to 6. It ...
- 2,450
2
votes
1
answer
392
views
How is the tree colored?
Not relevant fiction context
Paul's journey in the mathematical forest began this early morning. You know, he is a Biomathologist!
He saw a lot of spectacular plants, geometrical flowers and fractal
...
- 841
-4
votes
2
answers
155
views
If ABCDE*4 = EDCBA. A,B,C,D and E are all natural numbers ( 1-9) without repeating any natural number. Why is it deducible that E cannot be three?
If ABCDE*4 = EDCBA. ABCDE,EDCBA are five digit numbers. A,B,C,D and E are all natural numbers ( 1-9) without repeating any natural number. Why is it deducible that E cannot be three?
- 21
9
votes
4
answers
2k
views
Where to start with a large crack the lock puzzle like this?
Below is a puzzle called crack the lock. The rules are simple:
the lock contains 16 characters in this particular puzzle
No character can be used twice
the two numbers on the the far right tell you ...
- 129
-1
votes
1
answer
136
views
Can the solution a) of the accepted answer to the "Camels crossing a bridge" problem be extended to arbitrarily many camels?
This problem (and solution) with 5 camels each was posted here on Puzzling several years ago:
Two merchants have 5 camels each. One fine day, one of the merchants sells all of his goods in the market ...
- 11
2
votes
3
answers
332
views
Finding a 3-digit passcode from 4 mastermind clues
What is the logic used to solve this problem?
5
votes
1
answer
247
views
Logic in the Polycule
Heavily based on a puzzle from Brainteasers and Mindbenders.
Eve's anniversary with her polycule is tomorrow, and she's bought presents for all of her partners. However, she stashed the presents in ...
- 3,730
4
votes
1
answer
195
views
Fill the circles with the numbers 4, 5, 6, ... 10
Using all the numbers 4, 5, 6, ... 10 exactly once, fill each empty circle with a number so that if two numbers are in circles that are joined by a line then their difference (in absolute value) is at ...
- 5,956
1
vote
1
answer
268
views
Fox and rabbit on a circle
There are five holes in a line. One of them is occupied by a rabbit. Each night, the rabbit moves to a neighboring hole, either to the left or to the right. Each morning, a fox gets to inspect a hole ...
- 11
11
votes
1
answer
351
views
An Infinitude of Perfidious Pupils
Here's an original puzzle I created. Enjoy!
A teacher had infinitely many students, and he referred to them by the designations $\text{Student } 0$, $\text{Student } 1$, $\text{Student } 2$, and so on....
- 573
15
votes
1
answer
587
views
Operator! Some Product!
Happy Venndredi all,
A relatively straightforward one! The three overlapping ellipses form seven curved regions and there are seven tiles. Your task is to place exactly one tile per region so that ...
- 3,262
12
votes
1
answer
485
views
Tropical Rhythms
This is part 29 of the puzzle series Around the World in Many Days. Each part is solvable on its own.
Dear Puzzling,
This is a diagramless crossword. The clues are not numbered according to their ...
- 76.4k
36
votes
2
answers
1k
views
An Infinitude of Deceptive Devourers
Here's an original puzzle by me. I hope you enjoy!
A mother had infinitely many children, with the following names:
$\text{Albert}_1$, $\text{Albert}_2$, $\text{Albert}_3$, … , $\text{Beth}_1$, $\text{...
- 573
8
votes
1
answer
458
views
Twelve friends born on month ends
Twelve close friends were born on the last dates of their respective birth months. Fascinatingly, their birth months are different.
On 30th June 2023, all twelve of them had gathered for the birthday ...
- 5,685
0
votes
1
answer
239
views
Airlines Frequency puzzle
Source: It is from a book of logical reasoning questions, the name of which I am not able to verify.
Five airline companies P, Q, R, S and T applied to government permission to run their flights in a ...
- 113
1
vote
1
answer
182
views
Jacket Problem: Why So Sure? [duplicate]
Three girls graduating high school named: Eshal, Stacy, and Bridgette are playing a probabilistic game where they need to wear jackets of two colors: Bear Brown and Milk White. Initially, their eyes ...
- 147
10
votes
6
answers
3k
views
Knights and knaves not on an island
On a fictional island there were two types of people: knights who always told the truth, and knaves, who always lied. They got irritated by people asking them so many questions so they all moved to ...
- 5,956
8
votes
2
answers
570
views
12 logicians each have a number written on their foreheads
12 logicians each have a number written on their foreheads, visible to all but themself. One day, a meta-logician comes by and remarks, "I see all the numbers are distinct natural numbers." ...
- 6,418
31
votes
2
answers
8k
views
Is this Hashi puzzle unsolvable?
I found this puzzle in my dad's bathroom. The book is "Things To Do While You Poo On The Loo". I think the puzzle is malformed. Here is a Penpa link to an online solver. Is there actually an ...
- 504
5
votes
1
answer
834
views
How did she do that?
The King wants to test his 2 very smart advisors Sadin and Lena. In the courtyard he sets up 4 closed wooden boxes on a table. All are the exact same size. In front of each box there is a name plate.
...
- 5,447
2
votes
2
answers
302
views
Did Martin die by suicide, murder or accidental death?
One day, the police find Martin's body and locate 3 suspects to record their statements:
Alice: If Martin died of murder, then the murderer is Bob.
Bob: If Martin died of murder, then the murderer is ...
- 928
16
votes
4
answers
3k
views
Do you know where your number ranks among your peers?
A group of logicians each have a number written on their foreheads, visible to all but themself. One day, a meta-logician comes by and remarks, "I see all the numbers are distinct natural numbers....
- 6,418
6
votes
1
answer
303
views
The Nine Gardens Of Eden
This puzzle is part of the Monthly Topic Challenge #11: Now in 3D.
There are nine distinct known three-cell Garden of Eden patterns in the Life Without Death cellular automata, including the two well-...
- 2,699
2
votes
1
answer
498
views
Is Sumplete always analytically solvable?
I am stuck here at Sumplete.
I have tried looking for numbers that must be used/must not be used using https://combinationsumcalculator.com/ and all of them are either not used in all combinations (...
- 121
8
votes
1
answer
494
views
Variant of Abby and Bob and 3 numbers on the blackboard
Abby selects a positive integer $A$, and Bobby selects a positive integer $B$.
They then both tell their number secretly to Summy.
Summy writes the numbers $5$, $8$, and $15$ on the blackboard, and
...
- 2,818
-3
votes
2
answers
297
views
Is there an answer to this 'turning my fan off' puzzle?
I have a ceiling fan with 4 states. The states always go in the order of off, high, medium, low, off. A cord pull will change the state.
One pull of a cord to turn the fan to the off state from the ...
7
votes
1
answer
373
views
Next logical move in Heyawake
I'm just starting out on Heyawake. On this puzzle, I didn't see the next logical move, so I tried the 3 box with LRL and then RLR and I didn't have any luck going down those bifurcations. What am I ...
- 71
-3
votes
1
answer
391
views
Entry and Exit of people in pizza delivery shop
Similar problem at: https://brainly.in/question/38234304
Five people went to a pizza delivery shop at different times on a Sunday morning.
They spent exactly 15 mins, 16 mins, 20 mins, 25 mins and 35 ...
- 111
1
vote
3
answers
1k
views
How many students in this Math circle and can they together explain the solution of all of the 20 problems?
A Math circle leader assigned 20 problems as homework. At the next meeting, he found out that each student solved exactly 2 problems, and that each problem was solved by exactly 2 students.
A) How ...
- 2,818
-2
votes
1
answer
187
views
The Island of Arbitrary Puzzles [closed]
One day, an eccentric billionaire who’s obsessed with puzzles decides that he needs to open a theme park based on them. After throwing money at the problem for a few years, he finally finishes. ...
1
vote
1
answer
264
views
David's Three sisters
I came across this in an AI test and found it rather amusing to think about.
David has three sisters. Each of them has one brother. How many brothers does David have?
- 203
0
votes
0
answers
75
views
Two doors and two guards (variant) [duplicate]
So, I've finished building my "Island of Logic!", where there are a number of puzzles for travellers. So far, I have a bunch of rivers with river craft, wolves, goats, and cabbages; and a ...
- 296
-3
votes
2
answers
212
views
In relation to "the two door riddle," what is which door either guard is guarding logically dependent upon?
Link to the two door riddle: https://nerdist.com/article/how-to-beat-the-labyrinth-two-door-riddle/
Question: In relation to "the two door riddle," what is which door either guard is ...
4
votes
2
answers
301
views
An adjacent puzzle
Based on the information below, what numbers should replace A-D? Everything you need to know is there.
A, B, C, D are all integers. A and B are consecutive integers. B and C, C and D are not ...
- 30.1k
0
votes
1
answer
304
views
Help with slitherlink honeycomb [closed]
This is the best I can do:
It makes me think that I'm missing some simple detail.
- 27
1
vote
1
answer
256
views
Matrix puzzles from IT site [closed]
The puzzles comes from this site https://www.sweclockers.com/forum/trad/1602971-logik-test. Can anyone give a consistent explanations?
In the first puzzle, my mind is stuck on the last row's middle ...
- 151
20
votes
6
answers
2k
views
A harder version of a Richard Hess logical hat problem
In the July/August 2021 issue of MIT Technology Review, there was a "logical hat" problem by Richard Hess in the Puzzle Corner. I noticed that it could be generalized. Here is the "next ...
- 511
0
votes
0
answers
63
views
Three-bulb defusal dilemma [duplicate]
Here's a fun riddle I thought I'd share with you all:
You are an American military soldier who needs to defuse a catastrophic explosive set to go off in five minutes. You can do this by deactivating ...
13
votes
1
answer
801
views
In It for the Long Haul
This is part 22 of the puzzle series Around the World in Many Days. Each part is solvable on its own.
Dear Puzzling,
The light grey numbers and arrows from a Yajilin puzzle. Shade some cells in the ...
- 76.4k
11
votes
1
answer
987
views
Laughing At The Wrong Time
Uh...
Every letter corresponds to a different digit and 0 cannot be a leading digit.
Find $HA+UH$ if $$\begin{array}{cccc}
& H & A \\
+ & H & A \\
+ & H & A \\
+ & H &...
- 331
11
votes
2
answers
374
views
Orthogonally connecting even sudoku digits avoiding squares
Is there a way to complete a sudoku where you have to make sure all even digits are orthogonally connected to all the others, while avoiding 2x2 squares of even digits?
It is known to be possible when ...
- 113