# Questions tagged [puzzle]

This tag is meant for questions about the mathematical principles behind games, riddles, or their possible solutions. If the answer is known to you please do not use this tag to "riddle" other users, but rather to ask about the correctness of a possible solution or ways to extend and improve an existing solution.

338 questions
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### Taking Seats on a Plane

This is a neat little problem that I was discussing today with my lab group out at lunch. Not particularly difficult but interesting implications nonetheless Imagine there are a 100 people in line to ...
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### Riddle (simple arithmetic problem/illusion)

I'm not sure how well known this "riddle" is but here it goes. 3 people go to a restaurant, each buy food worth 10.00. When they're done, they give 30.00 to the waitress. She gives the money to the ...
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### Any smart ideas on finding the area of this shaded region?

Don't let the simplicity of this diagram fool you. I have been wondering about this for quite some time, but I can't think of an easy/smart way of finding it. Any ideas? For reference, the Area is: ...
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### Logic problem: Identifying poisoned wines out of a sample, minimizing test subjects with constraints

I just got out from my Math and Logic class with my friend. During the lecture, a well-known math/logic puzzle was presented: The King has $1000$ wines, $1$ of which is poisoned. He needs to ...
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### 3 Utilities | 3 Houses puzzle?

There's a puzzle where you have 3 houses and 3 utilities. You must draw lines so that each house is connected to all three utilities, but the lines cannot overlap. However, I'm fairly sure that the ...
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### Variation on the Monty Hall Problem

Many of us know the Monty Hall Problem But the other day I was asked a variation of this riddle. The answer of the original question is, of course, $66\%$ in favor of changing doors, but this is ...
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### How many triangles

I saw this question today, it asks how many triangles are in this picture. I don't know how to solve this (without counting directly), though I guess it has something to do with some recurrence. How ...
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I was given this problem 30 years ago by a coworker, posted it 15 years ago to rec.puzzles, and got a solution from Barry Wolk, but have never seen it again. Consider the series: $$1, \frac{1}{2},\... 4answers 35k views ### How many distinct ways to climb stairs in 1 or 2 steps at a time? I came across an interesting puzzle: You are climbing a stair case. It takes n steps to reach to the top. Each time you can either climb 1 or 2 steps. In how many distinct ways can you ... 4answers 22k views ### Finding the n-th lexicographic permutation of a string I have an ordered set of symbols S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }. I want to find the 1,000,000-th permutation in lexicographic order of S. It is a programming puzzle, but I wanted to figure out a ... 3answers 2k views ### Optimal algorithm for finding the odd sphere with a balance scale Say we have N spheres indexed as 1,2,3,\dotsc, N such that all of them have identical weight apart from one. We have to determine which sphere has the odd weight using just a balance scale. We ... 2answers 4k views ### After swapping the positions of the hour and the minute hand, when will a clock still give a valid time? At 12 o'clock, the hour hand and minute hand of the clock can be swapped, and the clock still gives the same time, but at 6 o'clock, it can not be swapped. So in what cases when we swap the hour and ... 7answers 5k views ### The final state of 1000 light bulbs switched on/off by 1000 people passing by There are 1000 light bulbs and 1000 tutors. All light bulbs are off. Tutor 1 goes flipping light bulb 1,2,3,4... tutor 2 then flips 2,4,6,8... tutor 3 then 3,6,9...etc until all 1000 tutors have ... 4answers 2k views ### x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} show that x=-c/b when a=0 OK, this one has me stumped. Given that the solution for ax^2+bx+c =0$$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\qquad(*)$$How would you show using (*) that x=-c/b when a=0 (Please dont use a=0 ... 24answers 18k views ### 100 blue-eyed islanders puzzle: 3 questions I read the Blue Eyes puzzle here, and the solution which I find quite interesting. My questions: What is the quantified piece of information that the Guru provides that each person did not already ... 7answers 31k views ### Famous puzzle: Girl/Boy proportion problem (Sum of infinite series) Puzzle In a country in which people only want boys, every family continues to have children until they have a boy. If they have a girl, they have another child. If they have a boy, they stop. What is ... 4answers 9k views ### What is the name of the logical puzzle, where one always lies and another always tells the truth? So i was solving exercises in propositional logic lately and stumbled upon a puzzle, that goes like this: Each inhabitant of a remote village always tells the truth or always lies. A villager will ... 2answers 1k views ### What is the minimum number of locks on the cabinet that would satisfy these conditions? Eleven scientists want to have a cabinet built where they will keep some top secret work. They want multiple locks installed, with keys distributed in such a way that if any six scientists are present ... 6answers 11k views ### Is there no solution to the blue-eyed islander puzzle? Text below copied from here The Blue-Eyed Islander problem is one of my favorites. You can read about it here on Terry Tao's website, along with some discussion. I'll copy the problem here as ... 1answer 4k views ### Fly and Two Trains Riddle Two trains travel on the same track towards each other, each going at a speed of 50 kph. They start out 100km apart. A fly starts at the front of one train and flies at 75 kph to the front of the ... 3answers 3k views ### How Strong is an Egg? You have two identical eggs. Standing in front of a 100 floor building, you wonder what is the maximum number of floors from which the egg can be dropped without breaking it. What is the minimum ... 2answers 6k views ### why 64 is equal to 65 here? [duplicate] how is this possible? I know there is some trick, should someone please explain?! 2answers 798 views ### Name Drawing Puzzle There is a party with 20 people, and everyone writes their name down on a piece of paper and puts it into a bag. The bag is mixed up, and each person draws one piece of paper. If you draw the name ... 3answers 498 views ### Maximize :: A = B \times C Given A = B \times C Using any 9 digits form two numbers B and C.All digits must be used exactly once. What is the maximum possible value of A? 2answers 24k views ### Predicting Real Numbers Here is an astounding riddle that at first seems impossible to solve. I'm certain the axiom of choice is required in any solution, and I have an outline of one possible solution, but would like to ... 2answers 940 views ### Guessing a subset of \{1,…,N\} I pick a random subset S of \{1,\ldots,N\}, and you have to guess what it is. After each guess G, I tell you the number of elements in G \cap S. How many guesses do you need? 6answers 12k views ### A three-way duel (probability puzzle) This puzzle is taken from Mathematical Puzzles: A Connoisseur's Collection [Peter Winkler]. I don't understand the solution. Alice, Bob, and Carol arrange a three-way duel. Alice is a poor shot, ... 6answers 11k views ### 100 prisoners and a lightbulb 100 prisoners are imprisoned in solitary cells. Each cell is windowless and soundproof. There's a central living room with one light bulb; the bulb is initially off. No prisoner can see the light bulb ... 5answers 6k views ### Better than random I have been trying to solve this question, but in vain. Please help. You are given two boxes with a number inside each box. The two numbers are different but you have no idea what they are. You ... 2answers 2k views ### Frog Jump Problem Lotus leaves are arranged around a circle. A Frog starts jumping from one leaf in the manner described below. In the first jump it skips one leaf,next jump it skips two,three the next jump and ... 1answer 793 views ### Integers and integer functions Let \Bbb{Z}^+be the set of all non-negative integers where n and k are given natural numbers. We consider the following non-decreasing function,$$f:\Bbb{Z}^+ \to \Bbb{Z}^+ such that \begin{...
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Okay, so this question was bound to come up sooner or later- the hope was to ask it well before someone asked it badly... We all love a good puzzle To a certain extent, any piece of mathematics is a ...
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### reversing digits and squaring

If we reverse the digits of $12$ we will get $21$. $12^{2}=144$. If we reverse its digits we will get $441$ which is $21^{2}$. Here is the puzzle. How many such two digit numbers are there? Digits ...
inradius = $5$ possible triangle sides $(25, 20, 15)$ $(37, 35, 12) (39, 28, 17)$ ... Find formula to find other possible sides of triangles.