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 ...

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9
votes
3answers
1k views

What is the mathematical explanation for this trick?

I found the following method to find one's age. It is working exactly for my case. I like to understand and solve this puzzle. If this is wrong forum, my sincere apologies. Please guide me solve this. ...
0
votes
2answers
29 views

Formula to have have a nonnegative integer go > 0 and < 127 [on hold]

I'm working on a digital music composition where I have nonnegative integer x. I need a formula to translate x into a nonnegative integer between 0 and 127. Any ...
4
votes
9answers
338 views

Propositional logic problem about a conversation of four people who lie or tell the truth

This is obviously elementary but can't figure it out. I am taking a course named Logic and Introduction to Analysis next semester and wanted to do some reading beforehand but to figure out how deep ...
1
vote
1answer
46 views

Find the Prize With a Limited Number of Questions

This question is the final step to a much more complicated question that I have spent many hours thinking about but was never able to solve so I am hoping someone here might be able to help. The ...
-1
votes
0answers
79 views

Find the highest story from which an egg can be dropped without breaking it (lowest average, not worst-case scenario) [on hold]

EDIT: Not looking for worst-case scenario solution, but rather the lowest average. This question has been answered many times for worst-case scenario being 14, I know this already :) PROBLEM: You ...
0
votes
1answer
44 views

Fibonacci Numbers in Nature

Supposedly the Fibonacci sequence appears naturally in nature, and my question is how, where and I guess why? I read that one way this is so is that it models the population of honey bees under ideal ...
4
votes
0answers
76 views

Adding Numbers Pattern

A few nights ago I couldn't sleep and so started doing this: I would take a number and add up all of its digits to get a new number and then add up all of those digits and so on until there was only ...
15
votes
2answers
2k views

Interview puzzle with a deck of cards, some cards upside-down

You are sitting in a dark room. It is completely dark. You can't see anything and there is no way that you can make light. Basically, just assume that you are blind for this task. There is a table in ...
-2
votes
0answers
39 views

Is my solution correct

I saw this question on a page: A kangaroo occupies an area of $50$ square centimetres and has a volume of $250000$ cubic centimetres. The kangaroo is $16$ metres away from a fence. Assume the ...
-3
votes
1answer
27 views

How many bit string of lenght 10 have [closed]

How many bits can a string of length 10 have? exactly threes 0's more 0s than 1's at least seven 1's at least three 1's
1
vote
2answers
37 views

Maximum possible parts of a cake if cut n times

In how many maximum/minium parts can a round cake($\large\text{ cylinder}$) be divided with $n$ cuts when each cut is necessarily a straight line? What would be the case if we have a ...
21
votes
1answer
1k views

Is every factorial divisible by its sum of digits?

Denote by $\Sigma_d(t)$ the sum of digits in the decimal representation of the number $t$. Prove / disprove: $$\forall n\in \mathbb N:\ \ \Sigma_d (n!) | n!$$
1
vote
1answer
12 views

Lexicographical rank of a string with duplicate characters

Given a string,you can find the lexicographic rank of a string using this algorithm: Let the given string be “STRING”. In the input string, ‘S’ is the first character. There are total 6 characters ...
5
votes
3answers
224 views

Calculating probabilities in horse racing!

I've seen a few similar threads to this on different forums but they don't seem to conclude to a satisfactory answer. My question is this: If you have 3 horses, A, B, and C and you know the winning ...
1
vote
1answer
57 views

How much distance did messenger cover? [closed]

A column of troops $80$m long is moving along a straight road at a uniform pace. A messenger is sent from the head of the column, delivers a message at the rear of the column and returns. He also ...
0
votes
4answers
105 views

how many words can be formed using all letters in the word EXAMINATION

Assuming any sequence of letters is a word, how many words can we form in such a way that the first two letters are different consonants while the last two letters are vowels?
0
votes
2answers
51 views

Find radius and height

I have the following problem: given the length of the chord AB and the length of the arc AB, find the radius of the circle and the height of the triangle ACB where C is a point on the circle such that ...
1
vote
1answer
45 views

Is it possible to create a bigger square using distinct smaller ones?

Another user just inquired about possible solutions to the famous $70$x$70$ square puzzle. When I encountered that many years ago and the first idea that came to my mind as to why I wouldn't think it ...
0
votes
3answers
81 views

Lightbulb puzzle related to proofs by induction.

The puzzle question was as follows: There is a circle of $n > 2$ lights with a switch next to each of them. Each switch can be flipped between two positions, thereby triggering the on/off states of ...
57
votes
5answers
9k views

Help me solve my father's riddle and get my book back

My father is a mathteacher and as such he regards asking tricky questions and playing mathematical pranks on me once in a while as part of his parental duty. So today before leaving home he sneaked ...
32
votes
6answers
2k views

Fun Geometric Series Puzzle

I recently was reminded of a puzzle I solved in college and thought I'd give it a shot again. However, being distanced from college math, I am having a harder time remembering how I arrived at the ...
-2
votes
1answer
90 views

The “Four beer caps” puzzle [closed]

Four beer caps are placed on the corners of a square table with arbitrary orientations. There is a robot on the table that acts upon three commands: (a) “flip a corner cap”, (b) “flip two diagonal ...
18
votes
2answers
1k views

A riddle with a witch and some gnomes

My question concerns a variation and a generalization of the following riddle. The Original Riddle: A wicked witch kidnaps 2 gnomes. She paralyzes them, and places a hat on each of their heads. Each ...
1
vote
1answer
65 views

Books in mathematics based on problem solving

Hi I'm looking for mathematical books that try to teach mathematical concepts by motivating and solving real life problems. For example a book in topology that is motivated by problems of planetary ...
13
votes
6answers
2k views

A strange puzzle having two possible solutions

A friend of mine asked me the following question: Suppose you have a basket in which there is a coin. The coin is marked with the number one. At noon less one minute, someone takes the coin ...
9
votes
1answer
95 views

Blocking lines of length $5$ in a $7 \times 8$ matrix; how can we know the solutions have a specific form?

A friend shared with me the following puzzle he encountered in a Chinese math competition: In a $7 \times 8$ matrix, we place tokens so that any straight line of length $5$ (horizontal, vertical, ...
40
votes
15answers
13k views

Interview riddle

On the Mathematics chat we were recently talking about the following problem @Chris'ssis had to solve during an interview : $$3\times 4=8$$ $$4\times 5=50$$ $$5\times 6=30$$ $$6\times 7=49$$ ...
-5
votes
0answers
79 views

Pirates And Coins No.2

this time the assumptions are same as the first question but this time there are six pirates and they have found just one coin the question is: the first pirate what will do?
2
votes
2answers
321 views

Pirates And Coins No.1

I actually like this one: There are five pirates in a ship and they have found 100 coins. The biggest pirate offers a way to divide the coins. If at least half of them agree on the division, it will ...
3
votes
1answer
79 views

Prove that there is only one way to make a square using all six tangram pieces

I am pretty sure there is only one way to make a square from the six tangram pieces: How can I prove this is the only way respecting all symmetries?
1
vote
0answers
25 views

A good book with algorithmic puzzles with solutions (not of kind “how to pass and IT interview”)

can you please advise me a book with algorithmic and mathematical (IT-oriented) puzzles. But I want not one more book of kind "How to pass an interview in Microsoft / Google / any other big company" ...
1
vote
1answer
46 views

How can I write a system of equations puzzle if given the solutions? (work backwards?)

\begin{matrix} a = 12 & b = 6 & c = 5 & d = 1 & e = 0\\ \end{matrix} How can I create a fun puzzle or word problem that would arrive at this solution above? For example, ...
1
vote
1answer
45 views

How to derive the answer for this puzzle problem visually?

I was looking at this problem on Puzzle StackExchange about working out the proportion of sand in two separate beakers. Rather than providing a mathematical explanation, I thought it would be easiest ...
1
vote
2answers
71 views

The defective doyle

There are six cans each containing doyles(each doyle weighs a gram), out them any of them can be defective. How can we find the defective cans in one weighing? and if each can has only two dozen ...
0
votes
2answers
93 views

Advanced Counting Puzzle

Suppose we have a house in which every room has an even number of doors. Prove that the number of doors from the house to the outside world is also even.
5
votes
2answers
59 views

Non-geometric way to calculate expected value of breaks?

In "50 Challenging Problems in Probability", question #43 is the following: "A bar is broken at random in two places. Find the average size of the smallest, of the middle-sized, and of the largest ...
3
votes
6answers
321 views

Puzzle about technique of fair using of unfair coin

There is an unfair coin. It tends to land on one side more than on the other. It is unknown which side is it. There is Mr. A and Mr. B. They argue about something and they want to use that coin to ...
0
votes
2answers
30 views

Puzzle about subjects, classroom numbers and teachers who teach those subjects in classrooms

A,B,C,D,E are teachers who may teach: math, physics, chemistry, biology or geography(one subject per person, we don't know who teaches what). They teach in classrooms 110,111,112,113,114. Tell which ...
2
votes
2answers
72 views

Russian roulette should a player pull the trigger or spin the cylinder

Two men plays Russian roulette. In revolver there are 2 bullets in consecutive chambers( 2 bullets are in 2 chambers next to each other). One man spun the cylinder, pulled the trigger and he is fine, ...
1
vote
1answer
49 views

Find A,B,C,D consecutive numbers based on written addition formula

$A, B, C, D$ are consecutive digits: $B$ is greater by $1$ than $A$, $C$ is greater by $1$ than $B$, $D$ is greater by one than $D$. Four $X$s are digits $A,B,C,D$ in unknown order. Find $A,B,C,D$ ...
0
votes
1answer
68 views

Puzzle about phographers in Africa taking pictures of 2 Animals which name corresponds to last name of their friends

Leo Lion, Tom Tiger, Eddie Elephant, George Gazelle, Peter Panther, Luke Leopard were on photographic safari in Africa. Every photographer took a picture of 2 animals. Every of these 2 animals ...
0
votes
1answer
38 views

Different approaches for this problem (number in different bases)

I came across the following problem on a puzzle website the other day. A $3$ digit number is written $(xyz)_{10}$ in base $10$ and $(zyx)_9$ in base $9$. What is it? The website (which I think ...
0
votes
2answers
68 views

A question from a job interview: math function that returns the number of positive numbers.

Describe a mathemathical function that receives 5 parameters, And returns the number of positive numbers. $f(x_1,x_2,x_3,x_4,x_5)\to 5,4,3,2,1,0$ - according to the number of positive numbers. ...
5
votes
1answer
69 views

Drawing previously undrawn cards from a deck

Suppose you have a deck of $y$ cards. First, randomly select $y-x$ distinct cards and sign the face of each, then shuffle all the cards back in to the deck. Proceed as follows: Draw a card. If it is ...
3
votes
0answers
65 views

A game on a smaller graph

In this question Alice and Bob play a game on $K_{2014}$, Alice directing one edge, Bob directing $1$ to $1000$ edges with Alice trying to make a cycle. The proof that Alice can win depended on the ...
1
vote
4answers
86 views

Probability: A variant of the Monty Hall Problem

Monty has a new game it's like his old one but now there are no goats just one car hiding behind one of three doors and this time he doesn't know where the car is. To play you pick one of the three ...
-1
votes
0answers
24 views

The problem category of sudoku Puzzle solved by search algorithms

Good day everybody, Sudoku puzzle solvers have been categorized in the literature to: Deductive algorithms that perceive sudoku as a hard constraint satisfaction problem (CSP) or Boolean ...
1
vote
1answer
84 views

logic\math question [closed]

Hi, This is allegedly a very simple question....most of the people answered that the answer is 9=90. i claim that theoretically, you can't be 100% sure about the right answer because you don't know ...
11
votes
1answer
304 views

Additive functional inequality

The function $f:R_+\to R_+$ is continuously differentiable and increasing. Also, $f(0)=0$ and $f(\infty)=\infty$. Continuity and differentiability of higher orders can be assumed if necessary. ...
1
vote
4answers
88 views

Two children paradox : where is my reasoning wrong?

I hope here is the good place to be asking this. Apologies otherwise. The statement is as follow : "Ms Michu has two children. We know one of the two is a girl, we call that girl Ludivine. What is ...