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

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1
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2answers
29 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
45 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
11 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
58 views

Counting and Abstract Problem Solving [on hold]

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
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2answers
35 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
29 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
79 views

recommend math books [on hold]

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
32 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 ...
2
votes
0answers
137 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
0answers
131 views

How do find the numerical average of $x^x$ from $(-4,-2)$?

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
232 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
64 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
233 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 ...
3
votes
2answers
69 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 ...
207
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 ...
2
votes
1answer
50 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
28 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 ...
5
votes
1answer
168 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, ...
0
votes
0answers
28 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 ...
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. ...
0
votes
0answers
40 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 ...
39
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
94 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
61 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
74 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
59 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
24 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 $18$ ...
17
votes
3answers
388 views

How, if at all, does pure mathematics benefit from $2^{74207281}-1$ being prime?

So a couple of days ago the $17$ million digit number $2^{57885161}-1$ was beaten by the $22$ million digit number $2^{74207281}-1$ at being the largest known prime number. Are there any specific ...
0
votes
1answer
37 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 $½$ litre litre back to A from B ...
0
votes
0answers
49 views

Mr.Smith commute word problem. Solved through logic, where is the argument unsound?

Mr. Smith commutes to the city regularly and invariably takes the same train home which arrives at the his home station at 5 pm. At this time, his chauffeur always just arrives, promptly picks him up ...
1
vote
1answer
94 views

How do the roots of “$x^2 + bx + c$” change as $b$ is kept constant and $c$ is changed? [closed]

Consider the function $x^2 + bx + c$ How do the (real or complex) roots of the equation change if $b$ is held constant and $c$ is changed? I.e. Which patterns are evident? What would it look like if ...
2
votes
2answers
24 views

Measurement Question Related to a Race Car

I recently got this peculiar interview question, and I wanted some help figuring out how to reach an appropriate solution. Imagine that we have a race car that is driving on a $50$-mile-long race ...
2
votes
1answer
32 views

Trivia Crack Probability

In the game Trivia Crack, you answer a question with 4 possible answers. A "life line" you can use allows you to guess a second time if you were wrong the first time. What is the probability you will ...
3
votes
1answer
223 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 ...
12
votes
4answers
891 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 ...
3
votes
1answer
52 views

Find Three Mutual Friends in a Mathematical Society

I am having trouble with the following combinatorics/graph theory problem: A mathematical society has three divisions (Pure, Applied, and Statistics), and exactly $n$ mathematicians in each ...
0
votes
1answer
143 views

Maths Puzzle - Logic

Somebody asked me this puzzle, but they don't have answer to it. 1+2+3+4 = 61 2+3+4+5 = 52 3+4+5+6 = 51 4+5+6+7 = 50 7+8+9+10 = ? I want to know whether my reasoning and ...
13
votes
0answers
108 views

Every natural number in binary can be cut and added so that it is a power of $2$? [duplicate]

I was watching a google techtalk with Donald Knuth and he mentions for every binary number $\overline{a_1a_2a_3\dots a_n}$ there exists $c_1<c_2<\dots <c_r=n$ so that: ...
1
vote
1answer
47 views

Counting duplicates

I have been doodling around and have stumbled across the following problem: Say I have a set $p = \{p_1, p_2, p_3, ..., p_n\}$ where $p_i \in \mathbb{N}$ $p_i$ could represent the amount of a ...
0
votes
1answer
12 views

Getting X based on table values

I have a table of values; $$3.00 \mapsto 12.15$$ $$3.10 \mapsto 12.82$$ And I'd like to know an equation for getting the inbetween values. For example: $$3.05 \mapsto \frac{12.15 + 12.82}2$$ But ...
3
votes
3answers
78 views

Computing $2016$ using basic operations on the fewest integers, in sequence

Using the operators $$+,-,\div,\times,\exp,(,),!$$ what is the least $n$ to come up with the number $2016$ using the sequence of numbers $1,2,3,\ldots,n$ in that order. You cannot combine numbers, so ...
5
votes
1answer
64 views

Possible all-Pentagon Polyhedra

If a polyhedron is made only of pentagons and hexagons, how many pentagons can it contain? With the assumption of three polygons per vertex, one can prove there are 12 pentagons. Let's not make that ...
1
vote
0answers
37 views

$\exists\ n \gt 34131$ with more than $7$ odd divisors $d_i \gt 1$ such as when $d_i+1$ are accumulated in increasing order to $1$ the sums are prime?

In the same style as a previous test, I did a little test today looking for all the numbers such as the odd divisors, ordered in increasing order excluding $1$, when they are accumulated one by one to ...
1
vote
2answers
36 views

Ratio of even and odd divisors

I've been given of this problem: Let $r$ be an integer which has $k$ even divisors and $k-3$ odd divisors. Furthemore let $x$ denote sum of all even divisors and $y$ sum of all odd divisors. What are ...
0
votes
1answer
26 views

If a particular constant contains every single possible combination of numbers in it's decimal expansion, does it also contain itself?

If a particular constant $a$ contains every single combination of numbers in it's decimal expansion, does it then imply that at one point the series should also contain itself?
15
votes
1answer
198 views

Show there is an uncut square lying in a larger square cut by lines

I found this problem on Keith Ball's blog sometime ago but I've never really worked it out. Show that if a square is cut by two lines (shown above in green) then there is an uncut square at ...