Puzzles, curiosities, brain teasers and other mathematics done "just for fun".

learn more… | top users | synonyms (2)

15
votes
4answers
1k views

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:...
0
votes
1answer
29 views

Finding the speed [on hold]

Charles and Smith left a place abc at the same time and stated moving in the same direction.Charles speed was $15$ Kmph and Smith's speed was $12$ kmph.Half an hour later Anthony left the place and ...
12
votes
0answers
135 views

Is $2^{16} = 65536$ the only power of $2$ that has no digit which is a power of $2$ in base-$10$?

I was watching this video on YouTube where it is told (at 6:26) that $2^{16} = 65536$ has no powers of $2$ in it when represented in base-$10$. Then he - I think as a joke - says "Go on, find another ...
0
votes
2answers
29 views

Finding the time taken to complete the work

In a call centre, $6$ employees working for ten hours can complete a certain task. They started working at 11 am .They continued till 5 pm. After that, each hour one more employee is added till the ...
0
votes
1answer
27 views

Conversion of Excel formula back to written Formula…if possible!

I turn to you as a last resort, in the hope that you will forgive my Maths ignorance and help me with what may be a simple problem. Essentially, this involves converting an excel formula to written ...
1
vote
2answers
28 views

Figure out what to multiply a number by to get it to double after x times.

I'm trying to figure out if there is a way to calculate what to multiply a number by to get it to double after $x$ times. For example, the number $100$, would be $200$ after multiplying it by $m$ $7$ ...
1
vote
0answers
28 views

A game involving divisibility

Two players $A$ and $B$ play the following game. First $A$ fixes a natural number $N > 100$ but does not reveal it. Afterwards $B$ chooses another natural number $n > 1$ and asks $A$ whether $n$ ...
6
votes
2answers
113 views

What is the optimal route for visiting Pokéstops in Pokémon Go?

Okay, I've got a fun problem for you, which was not suited for the gaming stackexchange: Pokéstops are GPS locations with a certain radius. When you are in the radius, you can get certain ingame ...
3
votes
1answer
52 views

Best strategy for the first player in a game for two on a large checkered paper

Here's a puzzle that's been seating in the back of my head for quite a long time. The game is played on a grid of infinite dimensions; sufficiently large checkered paper. First player specifies ...
1
vote
0answers
42 views

The Jeep Problem with Equally Spaced Stations

Consider the following problem. A jeep can carry a maximum load of fuel of 1 gallon, and it travels $l$ miles with $l$ gallons of fuel. The jeep moves along a straight line, and is required to cross a ...
1
vote
1answer
80 views

The Jeep Problem and Nash's Friends

The classical jeep problem is the following. A jeep can carry a maximum load of fuel of 1 gallon, and it travels $l$ miles with $l$ gallons of fuel. The jeep moves along a straight line, and is ...
3
votes
2answers
41 views

Find the Wrong Student

There are 15 student in the class and each of them has a different number 1 to 15. Student #1: wrote the natural number on the board. Student #2 said : This number is divisible by my number(number ...
1
vote
1answer
32 views

On a possibility/impossibility of a certain twisted situation in a tournament

Recently I encountered the following puzzle: Consider a game for two players which can only result in a win of one of the players (no ties). Now $n$ players decided to play this game each with ...
1
vote
0answers
22 views

Knowing the rates of gain and loss, estimate the average amount.

This question was presented to me as such: Say that people grow 100 hairs a day and lose 100 hairs a day and hairs have a lifespan of 100 days. Estimate how much hair an average person would have. ...
4
votes
0answers
50 views

Division of a square and value of a disk

I cam across this problem and I really don't know how to solve it. So you start with a square that has value 1. You divide this square in 4 so that each new square has a new value, as given by the ...
0
votes
1answer
38 views

Probability of solution amongst a set of Diophantine equations

I have a set of Diophantine equations which I know only one equation has a single solution. I am trying to find a way to give probabilities to which equation contains the solution. For example, ...
1
vote
1answer
43 views

Shortest possible distance to locate an unknown road

You are stranded in the middle of a large desert and the only way home is a through a straight road, which unfortunately you do not know the location of. If the perpendicular distance from you to ...
0
votes
0answers
36 views

Bribing a friend for money (game)

Here's how the game works: I get a pay bonus. I'm so happy I decide to give away $100$ dollars to one of my $n>1$ friends. My friends try to bribe me to get the money for themselves; I'm a ...
1
vote
1answer
49 views

Is this a pure imaginary number?

I've met this formula and I need to demonstrate that it is purely imaginary (it has no real part). $\frac{1}{2}\log(-\exp(i2\pi q))$, //for a real "input" q. As I don't know much about maths, what I'...
0
votes
0answers
20 views

enumerating polyominos

Polyominoes are made by gluing together finitely many squares along their edges. They always have connected interiors, but are allowed to have holes. Enumerating polyominoes is a huge subject, and ...
2
votes
0answers
32 views

Weighted War - Game of Mind and Probability

Weighted War is a game of bidding, where: Both players have cards valued from $1$ to $11$ in their hands There is a third pile of cards from $1$ to $11$ face down on the table and shuffled,...
1
vote
1answer
32 views

Make y the subject of x = y/(y-z)

I'm struggling with this GCSE question, but I think I'm just being silly. I've removed the fraction, making it: x(y-z) = y And then tried removing the brackets, making it: xy-xz = y But I'm not ...
8
votes
1answer
65 views

How math help reduce terms and conditions of someone's dying wish?

Good morning everyone... This is my very first question here, so I apologise in advance for any wrongdoing which I possibly make unintentionally. So here is a little background story. I'm working at a ...
1
vote
1answer
52 views

The Thirty-one Game: Winning Strategy for the First Player

I am going through UCLA's Game Theory, Part I. Below is an exercise on page 6: The Thirty-one Game. (Geoffrey Mott-Smith (1954)) From a deck of cards, take the Ace, 2,3,4,5, and 6 of each suit. ...
0
votes
0answers
5 views

How can I interpret joint and conditional entropies?

Say I have three variables, X,Y, and Z. Joint Entropy of X and Y is greater than joint entropy of X and Z, what does it mean? and Similarly, conditional entropy of X and Y is greater than conditional ...
14
votes
1answer
290 views

What's the best way to catch wild Pokémon in Pokémon GO?

In the newly released Pokémon GO, one of the major activities of the game is to catch wild Pokémon. These Pokémon are shown in the "nearby" list and their "rough distance" (RD) to you can be 0, 1, 2, ...
3
votes
1answer
52 views

Sets of integers with few sums

Let $S$ be a finite set of integers. Denote by $S^{\leq k}$ the set $\{a_1+\dots+a_\ell : \ell\leq k, a_1,\dots,a_\ell\in S\}$ of sums of at most $k$ elements from $S$. What are best/worst cases for ...
1
vote
1answer
27 views

Recurrence equation for sequence of vectors

Consider recurrent formula for a sequence of numbers $(y_n)$ (either real or complex): $$a_k y_{n+k}+a_{k-1}y_{n+k-1}+\cdots+a_0y_n=\sum_{i=0}^k a_i y_{n + i} = 0$$ It's known that the exact explicit ...
57
votes
3answers
4k views

Does multiplying all a number's roots together give a product of infinity?

This is a recreational mathematics question that I thought up, and I can't see if the answer has been addressed either. Take a positive, real number greater than 1, and multiply all its roots ...
1
vote
2answers
30 views

Sum of slopes between points of concurrent normals to hyperbola is zero

Let $ A_1, A_2, A_3, A_4 $ be four points on the hyperbola $xy = 1$. Suppose that the normals to the hyperbola at these four points are concurrent, i.e. they intersect in a single point. Prove that ...
0
votes
1answer
44 views

Maximum Coin Changes That Does Not Add To a Dollar

What is the maximal amount of money attained from coins of 1, 5, 10, 25 cent denominations that none of its subset amounts to 100 cents? We can find the solution with exhaustive or naive dynamic ...
2
votes
0answers
45 views

Heegner Prime visualizations

The Heegner numbers are 1, 2, 3, 7, 11, 19, 43, 67, 163. The ring of integers $\textbf{Q}(\sqrt{-d})$ have unique factorizations. 1 gives the Gaussian integers. 3 gives the Eisenstein integers. 7 ...
1
vote
2answers
67 views

Bound on the value of $\binom{n }{n/2}$

I know the value of $\binom{n}{r}$ is maximum for $r=n/2$ if $n$ is even. I am in need to calculate the value of $\binom{n}{n/2}$. \begin{align*} \binom{n}{0}+\binom{n}{1}+\binom{n}{2}+\ldots+\binom{...
0
votes
1answer
47 views

Integer solution to the equation below

I wanted to know integer solutions to the equation (1/k1) + (10/k2) + (100/k3) + ..... + (10^18/k19) = 1 (where k1,k2,k3.... are integers) which I believe is ...
0
votes
1answer
32 views

Relative speed of minute hand in a clock

In a 12 hours clock: The minute hand has to chase the hour hand with a relative speed of 5.5 degrees/min what is the mathematical derivation of this relative ...
4
votes
0answers
52 views

Movie math, real or not? (Ghost busters trailer) [closed]

I was watching the ghost busters trailer, and I stopped on a frame containing 'quantum physics'. I wonder if all of this is meaningful math, or some of it is complete gibberish, to look smart. I see ...
1
vote
1answer
120 views

Hard polynomial question.

I stuck with the following question. Let $n\geq 1$, $A, B\in\mathbb{R}[x]$ be polynomials of degree $n+1$ and $n$, respectively. Let $a_i$ and $b_i$ be its roots, suppose they are all real and ...
1
vote
1answer
43 views

Is it possible to find an expression for the x-value of where the normal line to a function hits another function? (Picture shown)

I was dabbling in some recreational math and I stumbled upon this problem: Say there are two arbitrary functions $f(x)$ and $g(x)$. Create the normal line to $g(x)$ at $x_g$; now find an expression ...
-1
votes
4answers
47 views

Cryptogram Problem [closed]

Phil is thinking of a number less than 700. When he interchanges the ones and the hundreds digits, the number increases by 297. When he interchanges the ones and the tens digits, the result increases ...
0
votes
0answers
58 views

Throwing eggs from flooors, general case [duplicate]

The following problem and its solution is well-known: you have two eggs and you have to measure which is the first floor of a building (that has in this example 36 floors) from which if an egg is ...
0
votes
0answers
54 views

How can I understand the step by step calculations for the formula from the blog below?

I am studying clustering and found a useful article on the blog post here Finding the K in K-Means. But I am having difficulty in understanding the formulas below and how I can do step by step ...
14
votes
4answers
710 views

Smallest future date which involves no repetition of a digit in the format DD/MM/YYYY [closed]

What is the smallest future date which involves no repetition of a digit in the format DD/MM/YYYY for the year? What is your approach?
0
votes
0answers
24 views

Mean Square Displacement of Alternating Random Walk

Consider a 1D random walk with varying steps: the length of the steps is $A$ a fraction $\gamma$ of the time, and $B$ the rest of the time. If $\gamma = 0$, the mean squared displacement approaches ...
9
votes
1answer
181 views

What's the upper bound for sofa problem?

I have seen a claim that for the sofa problem, an upper bound for the area of a sofa is $2 \sqrt 2$, and that this can be proved by a "simple" argument. But I can't find a proof. What that argument? (...
4
votes
0answers
73 views

Formula on conference t-shirt: $\ell(\beta) = \sum_{i=1}^{N}y_i \sum_{k=0}^{K}x_{ik}\beta_{k}-\log\left(1+e^{\sum_{k=0}^{K}x_{ik}\beta_{k}}\right)$

I need some assistance figuring out what this formula signifies and what it does. It is from a shirt I got recently at a conference and am curious about it. Thanks! $$\ell(\beta) = \sum_{i=1}^{N}...
1
vote
0answers
16 views

Convex 4-polytopes requiring 6 or more colors

Projected into 3-D space, a convex 4-polytope looks like a collection of convex polyhedra. If any two convex cells sharing a face have different colors, how many colors are required? In the paper ...
6
votes
2answers
136 views

A weight problem

I am having a hard time solving the following puzzle. Could you please me to figure it out? A chemist has a set of five weights. She knows that it includes one 1-gram weight, and also one each 2-, 3-,...
2
votes
1answer
72 views

Real life illustration of the fact that rationals have measure zero

I wonder if there's any real world phenomenon that reflects the mathematical fact that $\Bbb Q^k$ has Lebesgue measure zero in $\Bbb R^k$, or put another way, the likelihood that we get a rational ...
1
vote
3answers
85 views

Is there a possible mathematical solution for this? [closed]

I have what might be considered an odd question. I want to see if I can find a formula/equation to help me with the following. I'm working in a software package that we are using to calculate fees. ...
16
votes
2answers
630 views

Minimal generating set of Rubik's Cube group

The Rubik's Cube group is generated by the six moves $\{F,B,U,D,L,R\}$. However, is this the minimal generating set for the group? In other words, can I simulate the move $F$ just by making the moves $...