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

learn more… | top users | synonyms (2)

7
votes
2answers
152 views

Chinese New Year Equation 2016 [on hold]

Note: This question has been put on hold. If you find it interesting or useful, please vote to reopen it (by clicking on "reopen" at the bottom of this post), so that others can post their solutions. ...
5
votes
1answer
41 views

Factor the matrix (scalar $\times A$) into permutations of $A$

Here's an example of $A . B = scalar \times C$, done with magic squares. The last square does not have a consecutive range of digits. Drop the magic square requirement. In $2\times2$ matrices we ...
2
votes
4answers
76 views

Suppose a function is expressed by: $f(x)=f(x+1) - f(x-1)$ and $f(16)=20 , f(20)=16$ What is $f(20162016)$?

Math quiz bee question Suppose a function is expressed by: $$f(x)=f(x+1) + f(x-1)$$ and $$f(16)=20 , f(20)=16.$$ What is $f(20162016)$? Attempt at solution: $f(17)+f(15)=20$ ...
0
votes
0answers
20 views

Does this resilience/resource scheduling analogy make sense?

A firend has recently presented an analogy for the rescheduling of Doctors (big topic in the UK atm) across a 7 day week as opposed to a 5 day week with a skelton staff at weekends - I'm ignoring ...
-3
votes
0answers
51 views

Aircraft - How much time was lost [on hold]

Just a fun question to solve for you guys :) In attempting from flying from city $P$ to city $Q$, an aircraft followed a course that was $10$ degrees in error, as indicated in the figure. After ...
18
votes
1answer
127 views

Is there any palindromic power of $2$?

My question is in the title: Is it possible to find $n≥4$ such that $2^n$ is a palindromic number (in base $10$)? A palindromic number is a number which is the same, independently from which ...
0
votes
0answers
16 views

Is $\sigma(2^r)$ a palindrome (in base $10$) for some $r > 2$, where $\sigma$ is the sum-of-divisors function?

(Note: This post is a bit related to this earlier MSE question.) The title says it all. Is $\sigma(2^r)$ a palindrome (in base $10$) for some $r > 2$, where $\sigma$ is the sum-of-divisors ...
0
votes
1answer
12 views

Write bounds for a quantity in terms of bounds on another quantity

I have an expression that gives me the bounds for a certain variable X in terms of another variable Y. How can I write these ...
1
vote
1answer
50 views

Taking away pocket money [on hold]

This is my fist post on Mathematics, so I hope my question isn't too trivial - you won't need a degree to answer this one! - but it's messing with my head.... Allow me to explain..... I'm helping my ...
12
votes
2answers
9k views

What is the best strategy for Cookie-Clicker-esque games?

Today, I stumbled across the game Cookie Clicker, which I recommend you avoid until you have at least a few hours of time to waste. The basic idea behind the game is this: You have a large stash of ...
2
votes
1answer
35 views

Puzzle. Transfer maximal coal using a train [duplicate]

We need to transfer coal from point $A$ to point $B$ using a train. There is $9000$ tonne at point $A$. The distance between point $A$ and $B$ is $3000$ km. Train can carry only $3000$ tonne included ...
4
votes
0answers
172 views
+50

How do find the numerical average of $x^x$ from $(-4,-2)$ without x-values that give a complex output?

I wanted to find the approximate average of all real points in $(x)^{x}$ from $[-4,-2]$. This means I am ignoring all real inputs that give a complex output and need average to be a real number. To ...
0
votes
1answer
33 views

Multiplying magic squares like matrices to hopefully arrive at another magic square

Well, the title actually describes what is the problem in question. I was just thinking a bit about magic squares and this question popped-up. It could be that it is not interesting but I do not see a ...
0
votes
1answer
40 views

There are two buckets A and B. [closed]

There are two buckets A and B. Initially A has 2 litres of water and B is empty. At every hour 1 litre of water is transferred from A to B followed by returning litre back to A from B half an hour ...
1
vote
2answers
34 views

Area of piece of paper folded around straight line of orientation $\theta$

Imagine drawing a straight line $l$ through the center of a square piece of paper with area $1$. Now fold the paper along that line. Q: What is the function for the area covered by the folded ...
1
vote
4answers
54 views

Finding the height of a Building at Night

EDIT: Method $1$ is false, as pointed out by Hetebrij. If it is night, how would one find the height of the building? By assuming I am trying to find the height of a building at night, I am ...
12
votes
4answers
925 views

Volume of 1/2 using hull of finite point set with diameter 1

It's easy to bound a volume of a half. For example, the points $(0,0,0),(0,0,1),(0,1,0),(3,0,0)$ can do it. The problem is harder if no two points can be further than 1 apart. Bound a volume of 1/2 ...
0
votes
0answers
18 views

Property of all k-dimesional shapes

A close friend showed me an intuitive pattern that given a k-dimensional convex polytope P, if one doubles every sidelength to generate a $P'$ it is possible to fit $2^k$ copies of $P$ within the ...
13
votes
1answer
634 views

Any other Caltrops?

This question has been edited. The regular tetrahedron is a caltrop. When it lands on a face, one vertex points straight up, ready to jab the foot of anyone stepping on it. Define a caltrop as a ...
-3
votes
1answer
59 views

Counting and Abstract Problem Solving [closed]

Suppose that you have a bucket holds fiv-sev c, and one holds tw-one c. How could you use them to measure out thre c of water?
1
vote
2answers
37 views

Connecting up boxes mathematically (Puzzle)

How would you connect each black box once to each colored box without any lines overlapping, this is racking my brain so please help. Note that you can move the boxes where ever you want. Maybe ...
1
vote
2answers
135 views

How to calculate x in formula $ y =\left( \frac{\frac{17000}{x+400}+8.5}{100}+ 1\right) x $?

I am not even sure how it's officially called (so not sure with tag to give it). As an example if you have a math problem $y = x + 1$. You have a $y$ value, but not $x$. To you revese the problem $y - ...
8
votes
7answers
3k views

The number of bottles of beer one can buy with $10, after exchanging bottles and caps [closed]

My answer to this question is 15, but my dad insists I am wrong. Who is right? $2 can buy 1 bottle of beer. 4 bottle caps can be exchanged for 1 bottle beer. 2 empty bottles can be exchanged ...
1
vote
1answer
380 views

Arithmetic progressions of perfect powers

Find the largest positive integer $n<100$, such that there exists an arithmetic progression of positive integers $a_1,a_2,...,a_n$ with the following properties. $1)$ All numbers ...
1
vote
0answers
33 views

square monotonic numbers

A monotonic number is a number in which the digits are in non-decreasing order. I found by computer that most of these numbers are squares of these numbers $$3 \ldots 34,3 \ldots 35,3 \ldots 37,3 ...
4
votes
2answers
85 views

recommend math books [closed]

So i completed an year ago my schooling and i am pretty good at maths well at my level and i am very interested in maths and want to learn as much maths as possible and i like stuff like number ...
3
votes
1answer
224 views

How to draw a Mandelbrot Set with the connecting filaments visible?

The M-Set is connected. But the M-Set viewers I’ve found create cool pictures that don’t really show the connecting filaments. This mini-Mandel beetle should be connected to a larger min-Mandel by a ...
72
votes
14answers
10k views

Can the golden ratio accurately be expressed in terms of e and $\pi$

I was playing around with numbers when I noticed that $\sqrt e$ was very somewhat close to $\phi$ And so, I took it upon myself to try to find a way to express the golden ratio in terms of the ...
0
votes
1answer
34 views

Is there a function that allows you to generate the highest multiple of a number below a certain boundary?

Say for example, that I want the highest multiple of 36 below 100. Is there a function that allows me to generate this with two arbitrary numbers?
-3
votes
5answers
92 views

Catherine is now twice as old as Jason but 6 years ago she was 5 times as old as he was. How old is Catherine now? [closed]

This is an IQ question. "Catherine is now twice as old as Jason but 6 years ago she was 5 times as old as he was. How old is Catherine now?" How to solve such questions? I think their combined age ...
16
votes
4answers
564 views

Find all bijections $\,\,f:[0,1]\rightarrow[0,1],\,$ which satisfy $\,\,f\big(2x-f(x)\big)=x$.

A friend of mine gave me the following problem: Find all functions $f:[0,1]\to[0,1]$, which are one-to-one and onto and satisfy the following functional relation: $$ f\big(2x-f(x)\big)=x, \tag{1} $$ ...
2
votes
0answers
140 views

How to find Misiurewicz Points without solving huge polynomials? (Mandelbrot Set)

Here is a plot of 17,723 Misiurewicz Points. The code below generates a set of polynomials u[m,n], the roots of which have periodicity (m-n) starting at iteration n. I stopped at 17,723 points ...
4
votes
3answers
235 views

Lifting a toilet seat without breaking urine stream

Yes, I know the title is bizarre. I was urinating and forgot to lift the seat up. That made me wonder: assuming I maintain my current position, is it possible for the toilet seat (assume it is a ...
5
votes
1answer
239 views

Hillary Clinton's Iowa Caucus Coin Toss Wins and Bayesian Inference

In yesterday's Iowa Caucus, Hillary Clinton beat Bernie Sanders in six out of six tied counties by a coin-toss*. I believe we would have heard the uproar about it by now if this was somehow rigged in ...
213
votes
8answers
12k views

The length of toilet roll

Fun with Math time. My mom gave me a roll of toilet paper to put it in the bathroom, and looking at it I immediately wondered about this: is it possible, through very simple math, to calculate (with ...
171
votes
2answers
14k views

Proving you *can't* make $2011$ out of $1,2,3,4$: nice twist on the usual

An undergraduate was telling me about a puzzle he'd found: the idea was to make $2011$ out of the numbers $1, 2, 3, 4, \ldots, n$ with the following rules/constraints: the numbers must stay in order, ...
3
votes
0answers
66 views

Making $66$ with $1,1,1,1,1$

How can one make $66$ with only $1,1,1,1,1$? You cannot combine these two numbers to make a new number, such as this: $66=11 \times (1+1+1)!$. This was inspired a game of dice that I used to play, ...
3
votes
2answers
70 views

How to find the formula for the sequence 1, 3, 6, 10, 15…?

Before I say anything, I have to say that this isn't an advanced mathematics question; I'm just a 15 year-old student, who came across a mathematical problem. I saw a picture displaying a "ingenious ...
1
vote
0answers
33 views

Variation of the opaque forest problem (a.k.a farmyard problem)

I was wondering about the following variation of the opaque forest problem (see here and there for previous questions) : What is the least length set of segments that will intersect every straight ...
5
votes
1answer
171 views

Continuous path inside the Mandelbrot set connecting i to zero?

This relates to another challenge Question about drawing Mandelbrot filaments. It is possible to compute a formula for a continuous path inside the Mandelbrot Set connecting c=i to c=0? Obviously, ...
15
votes
4answers
759 views

How many trees in a forest?

Some time ago I met a forester. He told that there are only larches and spruces in his forest. He also said that there are exactly $10$ spruces at the distance of exactly 1 km from each larch. Next, ...
2
votes
1answer
51 views

Mean number of distinct marbles drawn at least once before marble #0 is drawn

I'm trying to solve this probability exercise: You have 100 marbles numbered 0 to 99 in a bag. You repeatedly draw a marble from the bag (all marbles being equiprobable), note its number, and ...
16
votes
5answers
1k views

Is high school contest math useful after high school?

I've been prepping for a lot of high school math competitions this year, and I was just wondering if all the math I learn would actually mean something in college. There is a chance that all of it ...
2
votes
2answers
3k views

Determing the number of possible March Madness brackets

Is there a simple combinatorial explanation to derive the total number of march madness brackets? Would it be $2*(2^{16}*2^{8}*2^{4}*2^{2}*2)^{2}$ where the final squared takes into account both ...
2
votes
4answers
283 views

What is the sum of the numbers in the shaded circles?

Each of the 6 circles contains a different counting number. The sum of all 6 numbers is 21.The sum of the 3 numbers along each side of the triangle is shown in the diagram. so What is the sum of the ...
2
votes
1answer
24 views

Generating Infinite Set with Function Composition

I imagined myself today being infinitely small, standing on the inside of a closed and perfectly mirrored surface and holding a laser. Could this surface be shaped in some way where I could turn on ...
3
votes
1answer
30 views

Discovering how the number Mind Scanner mobile app works…

Yesterday I downloaded a mobile app.Many of you may have also seen it.The working is as follows- Think of any two digit number from 10-99 Sum up the digits of the number and subtract it from the ...
41
votes
4answers
5k views

Sharing a pepperoni pizza with your worst enemy

You are about to eat a pepperoni pizza, which is sliced into eight pieces. Each pepperoni will unambiguously belong to some slice (no pepperoni is "between" slices). The caveat is that you have to ...
3
votes
1answer
96 views

1995 USAMO Problems/Problem 2

I tried to solve this problem: A calculator is broken so that the only keys that still work are the $\sin, \cos, \tan, \sin^{-1}, \cos^{-1}, \tan^{-1}$ buttons. The display initially shows $0$. ...
1
vote
1answer
35 views

What is the growth relationship of the number of digits a number has as numbers increase?

To clarify the question, since I'm sure the wording is awkward: In the decimal number system, to get from 1 digit to 2, it takes n=10 numbers. To get from 2 to 3, it takes 90 more numbers added to n. ...