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

learn more… | top users | synonyms (2)

0
votes
0answers
15 views

Limiting points

For a system of coaxial circles why are there only 2 limiting points? Shouldn't there be infinite limiting points? After all system of coaxial circles are pairs of circles which have same radical ...
1
vote
1answer
65 views

Expected Value for Number of Consecutive Cards of the Same Suit

Here is the setup. Shuffle a deck of 52 cards so their order is random (i.e., determined by a uniformly distributed random variable). Now flip through the cards and find the maximum number of ...
0
votes
1answer
30 views

Using the Fibonacci sequence and deduction to prove… [duplicate]

Using the Fibonacci sequence and induction prove that $$F_{n-1}F_{n+1}-F_{n}^2 = (-1)^n, \space \space n=1,2,3...$$ My efforts so far: The basis holds for $n=1$ Induction step: ...
5
votes
0answers
86 views

Magic square 9, Amazons, and the 2-(81,9,1) design

Consider the following order-7 magic square. The rows, columns, and diagonals all add up to the same sum: 175. Also, all the broken diagonals add up to the same sum, making this a pandiagonal ...
8
votes
0answers
120 views

Limit approximation for $\pi$ in the four fours puzzle?

The four fours puzzle is a recreational math puzzle whose aim is to express whole numbers using four occurrences of the digit 4 and a specified set of operators. A common variety permits the ...
3
votes
1answer
74 views

Golf Problem Math [closed]

Hey guys i cant seem to draw the diagram for this. I dont understand this question at all. I got this triangle but i dont know how to solve it. I only have 2 sides on it and i cant use the sin/cos law ...
0
votes
1answer
31 views

Trignometry Building Problem

Ok guys this is one of the trig recrational problems i was doing and i cant seem to draw the problem right... Please help.. A surveryor standing 69 meters from the base of the bulding measures the ...
2
votes
2answers
59 views

Does probability depend on knowledge?

There is at least $2/3$ probability that this question is rather silly, but being an almost absolute beginner in Probability, I will ask it anyway. Consider the following problem, proposed at AIME ...
0
votes
1answer
77 views

Connection between 7 and 13 [closed]

While there have been many numbers that have been deemed 'lucky' or 'unlucky', 7 and 13 are two of the most prominently known. So, this had led me to wonder if there were any connections between 7 ...
1
vote
1answer
70 views

How many 10-letter words do not contain all the vowels

I can't find where I am overcounting in the problem How many 10-letter words do not contain all the vowels. What I do is to count all the words that have at ...
2
votes
4answers
105 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
39 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 ...
7
votes
2answers
194 views

Chinese New Year Equation 2016

In the spirit of Chinese New Year, here's a problem to commemorate the year. $\color{black}{\text{Solve the following equation for positive integers $a$ and $b$:}}$ ...
0
votes
0answers
25 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 ...
24
votes
1answer
337 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
1answer
13 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
58 views

Taking away pocket money [closed]

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 ...
5
votes
1answer
52 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 ...
1
vote
1answer
76 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 ...
1
vote
2answers
42 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
77 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 ...
0
votes
0answers
23 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 ...
-3
votes
1answer
61 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
53 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
0answers
38 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
120 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 ...
0
votes
1answer
36 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
100 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 ...
2
votes
0answers
145 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 ...
5
votes
1answer
301 views

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 ...
4
votes
3answers
254 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 ...
3
votes
0answers
73 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, ...
5
votes
1answer
274 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 ...
4
votes
2answers
86 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 ...
1
vote
0answers
46 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 ...
230
votes
8answers
14k 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 ...
2
votes
1answer
56 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 ...
3
votes
1answer
43 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 ...
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 ...
7
votes
1answer
189 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 $c=0$? ...
0
votes
1answer
45 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 ...
2
votes
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. ...
0
votes
0answers
45 views

Branch of mathematics that deals with… iterations?

Is there a branch of mathematics that would deal with the ideas like the following: How would you coat a rectangular area in paint with a paintbrush that has a finite length less than the length of ...
42
votes
4answers
6k 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
115 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
2answers
65 views

A Problem Involving Two Sentries

Consider two sentries that are patroling on a road that is 2 miles long. They are sent to points chosen independently and at random on the road. I want to find the probability that the sentries will ...
5
votes
0answers
85 views

Stacking circles

When I tried to stack 21 circles of radii $(30, 31, 32... 50)$ on top of each other in a tube (ID of $100$ wide), I thought they would reach the same height regardless of the order, however I was ...
4
votes
1answer
70 views

Probability that a number has $m$ indistinct factors

I just discovered Matlab's factor()-function, and I randomly typed in 20081294819, and to my surprise it only had two factors (5099 and 3938281)! I had expected many more factors for such a big number ...
0
votes
0answers
18 views

Graph grouping with geometric criteria

I start with a list of adjacent tetrahedra, where there are tight seals to one another along faces for two tetrahedra that are adjacent. The vertices belonging to these faces for both tetrahedra are ...
1
vote
1answer
26 views

Technical meaning of two alike combinatorial problems

I am confused in how to interpret two alike combinatorial problems, because to me they both look the same. These are the problems: How many ways are there to put $24$ distinguishable flags on $18$ ...