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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Two spies throwing stones into a river
There is a puzzle about two spies:
Two spies must pass each other two secret numbers (one number per spy), unnoticed by their enemies. They have agreed on a method for doing this using only 26 ...
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Knights and jokers
There are $N$ men. $K$ of them are knights, $M$ of them are jokers.
$N$ is known, $K$ and $M$ are unknown. You know that: $K + M = N$, $K \gt M$, $M \ge 1$, $N$ is odd.
Knights always tell the truth, ...
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How to create a pure mathematical-logical based puzzle equivalent to resistance based physical puzzle?
I am thinking how to reformulate a physical puzzle in a way that it becomes purely logic based (doesn't uses physical lows and can be solved by a person, who knows nothing about physics).
The puzzle:
...
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Is there a move-efficient way to rotate the center pieces on the Octo-Star?
I'm looking for a more efficient algorithm to rotate the center column of the Octo-Star puzzle 45 degrees.
The situation below occurs when four properly-oriented edges are next to each other, ...
user20
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How do you solve a word puzzle when you have no idea where to start?
When you're looking at a logical word puzzle, what sorts of clues should you try to look for to solve them? There have been quite a few puzzles posted to this site so far that I spent a few minutes ...
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Winning an unfair game
I came across the following interesting problem today:
A game consists of a sequence of plays; on each play either you or your opponent scores a point, you with probability 𝑝 < 1/2, he with ...
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You are a cat. How do you swap?
Number twenty-one cages containing mice, 1, 2, 3, etc., up to 21, and place them in the following order:
1 14 15 17 3 7 13 6 20 2 19 21 5 18 8 11 16 9 12 4 10
...
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Variation of 100 prisoners light problem
There is a classic problem below for which Dr. Yisong Song wrote a very well written and thought out series of solutions.
The variation here I've never seen anywhere but am curious. I want to work it ...
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Differentiate between the numbers from 1 to 5 with one single yes/no question
This question requires a bit of logical distortion to get the information required to answer the question.
However, I've never seen it asked before what would happen if more modes of question ...
user88
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Is it indeed impossible to score any points in the test in Heinlein's "Space Cadet"?
In Heinlein's Space Cadet, one of many tests administered to the protagonist seems to have no way of scoring any points. See the excerpt below.
Late in the day he was ushered into a cubbyhole ...
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Clock Puzzle problem
Today I came across this puzzle:
How many minutes is it until six o'clock if fifty minutes ago it was
four times as many minutes past three o'clock?
Any help?
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Are there any forms of patience or solitaire that can be solved by logic alone?
Single player games using a single deck of playing cards often called patience or solitaire, generally involve a degree of skill and luck to solve, with card shuffling ultimately being the deciding ...
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When and where was the first logic-grid-based puzzle published?
Logic puzzles with a set of conditions and a "logic grid" are very popular. More than one publisher is currently producing puzzle books with these types of puzzles.
A Wikipedia article claims ...
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You have one question to tell whether the number I'm thinking of is 1, 2, or 3
This is an interesting puzzle which was passed to me by a friend some time ago. I do know the answer, but will refrain from self-answering on this to see where it goes.
I'm thinking of a number: 1, 2,...
user20
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Are there 'Hexanum' puzzles that require advanced methods to solve? [closed]
The puzzle below features each week in a TV guide. It's called "Number Workout" there but I've done a bit of research and it seems to be called "Hexanum" elsewhere. It bears some resemblance to Sudoku,...
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Fastest way to cross a river: four people with different rowing speeds
This problem is commonly cited as a Microsoft interview problem, although I have paraphrased it here to involve a river and a boat instead of a bridge and a flashlight, and tweaked the crossing times ...
user88
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Hats and Aliens
Here's a neat little puzzle taken from a Google interview question:
10 humans are abducted by aliens; each represents 10% of the entire human population. The aliens give each abductee either a purple ...
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Could a gold/{second metal} crown the be created that would pass the Archimedes test cost effectively? [closed]
Many people are familiar with the story of Archimedes submerging a crown in water to identify if the volume of the crown was consistent with the volume of the same amount of gold. The test was to see ...
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I don't know the two numbers... but now I do
Two perfect logicians, Summer and Proctor, are told that integers 𝑥 and 𝑦 have been chosen such that 1 < 𝑥 < 𝑦 and 𝑥 + 𝑦 < 100. Summer is given the value 𝑥 + 𝑦 and Proctor is given ...
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In the 100 blue eyes problem - why is the oracle necessary?
The riddle
Randall Munroe (of xkcd fame) has, a bit hidden on his site, a logic puzzle:
A group of people with assorted eye colors live on an island. They are
all perfect logicians -- if a ...
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Is there a proof that a map of the United States requires 4 colors?
The Four color theorem states that no more than four colors are required for any map. Can it be proved or disproved that 3 colors can be used for United States map?
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How do I tell the children's ages?
My friend once told me a logic puzzle along the lines of:
A student asks a teacher what the ages of the teacher's three kids are. The teacher said, "the product of their ages is 72, and the sum ...
user20
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Guessing hat colors
Red or Black
There are 3 children sitting on three chairs. The children can only look forward and all wear one hat. The hats are either black or red. They are a total of 5 hats, 3 are colored red and ...
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Burning ropes as timers
You have 2 identical ropes which burn at a specific rate, and an unlimited supply of matches. When you light one end of a rope, the fire will take exactly 1 hour to travel to the other end of the rope....
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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 ...
user88
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Pirates and gold coins
A group of N pirates has come by a chest containing 200 gold coins. Their rules require that the coins be distributed by the following approach. The pirates are ranked from fiercest to meekest and ...
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The Puzzle of the Locked Box
Here's an old puzzle I found in a book once.
A box has some number of locks on it. It is guarded by a Grand Vizier and four slaves, each of which hold keys to the locks.
The Grand Vizier and slaves ...
user88
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Sliding Bolt Puzzle - fastest solution (time-wise)
This is a follow-up question for the Sliding Bolt Puzzle. If you have not solved it yet, you might want to head there first, as the extended discussion of its solution in this question will contain ...
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Round-Robin Tournament
20 teams played in a round-robin tournament.
The winner of each game got 1 point, and the loser got 0; there were no draws.
Each team's total score was a square number.
At least one team had a unique ...
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N logicians wearing hats of N colors
N logicians are wearing hats which can be of N different colors (each hat has one color; there can be multiple hats with the same color). Each logician can see the colors of all hats except his own. ...
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Sliding Bolt Puzzle
You are in a room with two adjacent doors locked by four sliding bolts. The bolts are movable and block only one door at a time; however, you do not know which bolt currently is blocking which door.
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What is the maximum number of solutions a Sudoku puzzle can have?
I've seen Sudoku puzzles that can be solved two different ways. Referring to a traditional 9x9 grid:
Is it possible for a Sudoku puzzle to have more than two solutions? If so, what is the maximum ...
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