Tagged Questions

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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2
votes
1answer
35 views

Best score in this puzzle

I want to maximise the score of the following table, choosing one item from each column/row, so no two items are on the same row or column. Score to maximise is just adding all the choices together. ...
4
votes
3answers
74 views

Puzzle: “Yes colour of my hat is white.”

There are $n$ people in room each being put on hat from amongest at least $n$ white hats and $n-1$ black hats. They stand in a queue, so that everyone can see the colour of the hat of the person ...
2
votes
2answers
28 views

Interview question - numbered tiles

Ok, this interview question interested me and I would love to see an explanation! There are some tiles: 1, 1, 2, 2, 3, 3 They must be placed in a straight line, such that there is one tile between ...
7
votes
0answers
119 views

Math puzzle: 10 digit strings generations

There was a question in a math competition that I attended last year. At the end of competition, I realized that my answer was wrong for the question below and I have never been able to figure out how ...
0
votes
0answers
25 views

find the given amount [on hold]

A confused bank teller transposed the dollar and cent when he cashed a cheque for Mark, giving her rupees instead of cent and cent instead of rupees. After buying a toffee for 50 cent, Mark noticed ...
3
votes
2answers
70 views

Who is the last person?

twenty five people are standing in a circle. starting with person 1, they count off from 1 to 7 and then start over with 1. each person who says "7" drops out of the circle. who is the last person ...
-4
votes
1answer
31 views

How many numbers which are ≤100 and whose unit digit is zero, are happy [on hold]

A number is said to be a happy number if on finding the sum of the squares of its digits, and then the sum of the squares of the digits of that sum, and so on, the process ends in 1. How many numbers ...
75
votes
10answers
8k views

Mathematician vs. Computer: A Game

A mathematician and a computer are playing a game: First, the mathematician chooses an integer from the range $2,...,1000$. Then, the computer chooses an integer uniformly at random from the same ...
0
votes
0answers
33 views

Alternative numbering system?

The markings below are on the right of page at http://lyca.com/story/ It seems pretty clear they are part of a numbering scheme since they appear at mostly regular intervals. This may be related to a ...
0
votes
1answer
28 views

Game of Life receptor

I am looking for an interesting structure in the game of life. If left alone, it shouldn't expand a lot(Still lifes or oscillators are allowed), but if we add an life somewhere, it launches an ...
14
votes
3answers
2k views

Largest prime number with all digits different

What is the largest prime with distinct digits? (It is certainly less than ten digits long.Can you explain it why?
1
vote
2answers
106 views

Two math professors problem

My friend asks me a question from internet. The question is as follows Two math professors, professor Uno and professor Dos, play chess at the park while reminiscing about their past. Prof. ...
1
vote
0answers
27 views

how to find if a number has a representation in a powerbase format?

I better explain this problem with an example, $100$ would be represented as $983$ because $9^1 + 8^2 + 3^3$ is one hundred. So how to find the relation between the number $n$ and numbers that can be ...
1
vote
3answers
43 views

Bridge-crossing puzzle [closed]

A group of four people is trying to cross a bridge. It is dark and they have to use a flashlight (which is available). No more than two people can cross the bridge simultaneously and it takes ...
1
vote
1answer
49 views

Why is the “rational” solution to the Traveler's Dilemma 2?

Traveler's Dilemma An airline loses two suitcases belonging to two different travelers. Both suitcases happen to be identical and contain identical items. An airline manager tasked to settle the ...
0
votes
2answers
109 views

Pigeon hole principle based puzzle question

A card-board box contains 12 pairs each of three different types of hand gloves used by batsman in cricket. They are separated into single units of gloves and all mixed. you can not see the gloves ...
1
vote
1answer
45 views

How to solve this knights and knaves problem using CNF?

There are 5 natives A-E, each is either a knight or knave. Let a be the statement “A is a knight” and ¬a be “A is a knave”. Same format for the other four natives. Let T be “tautology” and F be ...
0
votes
1answer
54 views

Using only addition, subtraction and multiplication

I have the numbers 6, 30, 8, 8, 3, 7, 1, 2, and 5. Using only addition, subtraction, and multiplication, can you use those numbers to make 60, 54, and 52?
4
votes
2answers
75 views

Walk on Earth: Math Puzzle

Here's the famous math puzzle posted by Prof. Walter Lewin about a person walking on earth, quoted below for posterity: A person stands on the North Pole. She walks 10 miles South, then 10 ...
0
votes
2answers
80 views

Biased coin flip from an unbiased coin flip

Von Neumman's method allows us to generate a fair coin flip from any unbiased coin flip using only two bits (two tosses) of information (http://en.wikipedia.org/wiki/Fair_coin). Is the reverse ...
0
votes
1answer
44 views

riddles and compound proposition

I've been learning about propositions and truth tables recently and been given examples like "If it is raining I will take my umbrella." P=it is raining Q=i take my umbrella. It's very easy to ...
1
vote
0answers
68 views

Proof that a common brain teaser is wrong (Burning Rope)

There is a common brain teaser that goes like this: You are given two ropes and a lighter. This is the only equipment you can use. You are told that each of the two ropes has the following property: ...
0
votes
0answers
35 views

Why is it true that $\forall b\in(0,1): (1-b)\left(e(1-b)\right)^{\frac{b}{1-b}}\geq\prod\limits_{n=2}^{\infty}n^{-b^n}\geq 0$

Why is it true that $$\forall b\in(0,1)$$ $$1\geq(1-b)\left(e(1-b)\right)^{\frac{b}{1-b}}\geq\prod\limits_{n=2}^{\infty}n^{-b^n}\geq 0$$ Note: Let $$f(x)=\prod\limits_{n=2}^{\infty}n^{-b^n}$$ Then ...
1
vote
3answers
42 views

Why this question can determine whether he is a knight or knave?

Knight always tell the truth, while knave always lies. If I ask this question:"If I were to ask you if you always told the truth, would you say that you did?" Why this question can determine whether ...
0
votes
1answer
726 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 ...
-1
votes
0answers
17 views

How to expand such expression?

There is an array $a_n\in K$ and mapping $f:K\rightarrow K$ with properties: $f(a_0)=a_0$ $f(a_n)=a_{n+1}-na_{n-1}$ ask how to expand $f^{(m)}(a_0)=f(f(f(f...f(a_0)...)))$ $\quad$ (do $f$ operation ...
3
votes
0answers
24 views

Given $n$, find $a,b$ such that $a+b=n$ and $\Omega(a)+\Omega(b)$ is maximized

Given a number $n$, find $a,b$ such that: $a,b$ non-negative integers $a+b=n$ $\Omega(a)+\Omega(b)$ is maximized $\Omega(n)$ counts the number of prime factors of n (with multiplicity). ...
2
votes
3answers
48 views

Why is this true? $\forall a\in(1,\infty), B\in(0,\infty), x\in(0,\infty) : a^x\geq \left(\frac{ex\ln(a)}{B}\right)^{B}$

I know $$\forall a\in(1,\infty), B\in(0,\infty), x\in(0,\infty)$$ $$a^x\geq \left(\frac{ex\ln(a)}{B}\right)^{B}$$ can be proved using AM-GM. Is there a simple way to show the inequality holds in all ...
4
votes
2answers
83 views

What comes next? For 8 year olds. Part II

This question is from the homework of my niece. She is 8 years old. And I could not help her with this question. There is a sequence of numbers. Problem asks the sum of the next two numbers. And ...
-1
votes
1answer
56 views

Is this dot puzzle solvable?

Is it possible to connect all the dots with one line without touching the same point, going diagonally, or touching the black line? • • • • • • • | • • • • • • • • • • • • • • • • • • • • • • • • ...
1
vote
2answers
60 views

Seating Arrangement puzzle.

Not sure if its a correct place to post these kind of questions. Eight persons-P,S,Q,R,U,B,J and C are sitting in a field in a circle. Three are facing opposite side and other five are facing the ...
2
votes
1answer
4k views

Probabalistic proof of green-eyed dragons logic puzzle

I came across the "green-eyed dragons" puzzle (alternatively known as the "blue eyed villagers" puzzle). The typical proof uses a straightforward inductive strategy. I came up with a probabalistic ...
4
votes
1answer
72 views

The best of Martin Gardner…

Martin Gardner's 100th Birthday is just about to come and I am a huge fan of his books as well as his puzzles and games . I personally loved his puzzles like the "Reversed Trousers" which said ...
0
votes
3answers
42 views

Simple equations word problem

In a three-digit number, the difference between its hundreds digit and its tens digit is equal to the difference between its tens digit and its units digit. Also the sum of the digits is $9$. How many ...
2
votes
2answers
81 views

Mind Teasers : Difficult Brain Twister (Today Challenge)

Question can be found in the link below Source: http://gpuzzles.com/mind-teasers/difficult-brain-twister/
0
votes
1answer
57 views

Nim Sum Game Variant

Suppose there are black and white balls in a box. The initial number of white balls is m and the initial number of black balls is n. This is a two player game. Each player can do the following taking ...
1
vote
2answers
49 views

Area of one of four regions within a rectangle

There is a figure below (a rectangle). You can see different colors depicting different regions of the figure. The labels on the top of a region defines the area of that region. Can you find the ...
1
vote
2answers
53 views

Probability interview question

Suppose we have three positive integers $A, B, C$. We randomly choose an integer $a$ in the range $[0,A]$ and an integer $b$ in the range $[0,B]$. Find the probability that $a + b\leq C$. I am unable ...
3
votes
1answer
51 views

Write $1681$ using four $4$s

Write $1681$, using $4$, four times only, and you can use any mathematical operation available within mathematics(except catenation or $4.4$ etc, it should be an operation), like factorial and cube ...
0
votes
2answers
68 views

Day of the week from the date.

I still remember when I was a kid some senior student used to ask us a date from history and then tell us what day was then within 20 seconds. I read montgomery's Number theory and when found the ...
1
vote
3answers
29 views

Finding the expectation value of a random variable counting the occurrences of certain events

Let there be $M$ (distinguishable) boxes and $N$ balls, which we uniformly distribute among the boxes. For $k \leq N$, let $g_k: \Omega \rightarrow \mathbb{Z}$ be the function counting the number of ...
22
votes
8answers
1k views

Google Interview Question about a town where if a couple has a girl born, they can't have more children… [duplicate]

Today I was reading about Google Interview math puzzles and I couldn't solve the following puzzle. Imagine a town where there is a law: If a couple have a girl born, then they can't have more ...
0
votes
1answer
76 views

What comes next? For 8 year olds

This question is from the homework of my niece. She is 8 years old. And I could not help her with this question. There are 5 x 3 cells. And there is a number in each cell. Problem asks what should be ...
2
votes
1answer
68 views

Find out the final survivor

A question one of my friend asked me: There are $n$ (he told me to find for $100$ people and then asked the general formula for $n$ people) people sitting at a round table. A person (say $1$) killed ...
3
votes
1answer
39 views

Good Book on Permutations and puzzles

I need to study about permutations to mathematically analyze scrambling of digital images. Do you know any good books on this matter ??
0
votes
1answer
47 views

An interesting puzzle for some, confusing for me

Suppose that $a$ is of odd order $k$ and $bab=a$. I need to show that $b$, must be of order $2$. We can prove this anyway we want to, but our hint is to expand $(bab)^k$ and re-associate and then ...
2
votes
4answers
954 views

Find a 4-digit number which, divided by a 3-digit number (all unique digits) equals 9

This question is related to this Stack Overlow post. I tried following R code to find a 4 digit number divided by a 3 digit number (all unique digits) so that result equals 9: ...
0
votes
0answers
27 views

problem solving strategy excerises

given 5 bowls with the following amount of balls inside: 1 in the first, 3 in the second, 5 in the third, 7 in the fourth, and 9 in the fifth. There are two players, each player in turn is permitted ...
1
vote
2answers
40 views

Can't find a logical formulation to this problem

In this problem are only truth tellers and liars. When meeting two people, A and B, you ask A: "Is any of you a truth teller?", to which A replies: "If B is a liars, then i'm a liar" What are A ...
5
votes
2answers
112 views

Construct numbers using digits $123456789$ and the operations $+,-,×,÷$

From an old book I found the following question. Use the digits $1,2,3,4,5,6,7,8,9$ and the operations $"+,-,×,÷"$ with $( )$ for construct the result $100.$ During the computations the order of ...