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

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0
votes
1answer
35 views

Calculating variable in math equation

I am not good with math, I have this equation (very simple to most) but I need help on how to get the value of x 10 = x - (1.29 + 4.99% of x) my question is how ...
9
votes
1answer
4k views

Proof Involving a Problem from “Good Will Hunting”

I don't know if any of you have seen the movie "Good Will Hunting" but there is a particular mathematics problem in the movie that is of interest to be. One of the problems used in the movie is "Draw ...
0
votes
1answer
168 views

12 base units instead of 10

Why do we use 10 as a whole unit when it can't be evenly divided by 3 or 6 without resulting in an infinite decimal I.e 3.3333etc. If units of 12 were used I.e 1 2 3 4 5 6 7 8 9 ? # 10. 3.3333 would ...
4
votes
1answer
156 views

Linear Algebra in curved space

We know that Euclidean geometry and Newtonian Physics are special cases that only work in a flat space-time. Got to thinking about linear algebra and matrices. Is linear-algebra a special subset of ...
6
votes
1answer
230 views

No primes in this sequence

Here's a fun little problem: Prove that the sequence $$10001, 100010001, 1000100010001, \cdots$$ contains no prime numbers.
3
votes
1answer
111 views

Guess the Polynomial

Player ONE has a finite degree polynomial $p$ with integer coefficients in mind whose domain is the reals. Player TWO gets to ask Player ONE to evaluate the polynomial at two points $x_0,x_1$ and ...
10
votes
1answer
3k views

How to prove the number of solutions to nine dots puzzle

The aim of the Nine Dots Puzzle is to draw a path connecting 9 dots arranged in a $3\times 3$ grid using 4 continuous straight lines, never lifting the pen/pencil from the piece of paper. A solution ...
3
votes
3answers
1k views

Minimizing perimeter given rectangle's area for 10-years-olds

I was recently in touch with some person from Russia how is busy with books for Russian elementary schools, in particularly I learned that now they give elementary set theory for the 2nd grade ...
3
votes
1answer
77 views

Minimal diameter of set of fractions

Let $p_n$ be a pairwise partition of $\{1,2,...,2n\}, n\in \bf N$ where $(a,b)\in p \implies a<b$, and $P_n$ the set of all such pairwise partition. $d(n) := \min_{p_n\in ...
0
votes
0answers
97 views

Did I make a “forced” interpretation?

Just a few years ago I wrote an article called The Geometry of the MRB constant. Since then I've wondered if there is a better, more natural geometric analysis of the following summation. $$ ...
1
vote
1answer
61 views

In what kind of Banach algebras is 0 the only topological zero divisor?

On page 33 of http://math.aalto.fi/opetus/harmanal/pruju/calg04.pdf it is asked in what kind of Banach algebras is 0 the only topological zero divisor. What do they mean by kind of Banach algebras. ...
5
votes
5answers
403 views

Leisure reading for an undergraduate student

I am a freshman at a local university. I never really had much passion for math, but I always did well in math exams . I attribute this lack of passion to rote learning/emphasis on methods/formulas ...
2
votes
1answer
68 views

Why all near integers

$C$MRB is a symbol for the MRB constant. Why do I get all near 0, 1 or 2 for all values of n for sin(Pi/$C$MRB*(5060936308 + 78389363/24*Floor(n)))? The results near 0 are very small and the ...
1
vote
2answers
59 views

Recursive formular and closed-form questions

Follow the question the $f(n)=4n-1$ and $F(n)=\sum_{k=0}^nf(k)$. And it ask you to write the recursive of $F(n)$. But I only know the recursive of $f(n)$ is $$f(n)=\begin{cases} -1,&\text{if ...
0
votes
1answer
87 views

Conditions for convergence of a geometric series [duplicate]

This question concerns the infinite geometric series formula. It turns out there is a nice formula for the sum of an infinite geometric series. Consider the infinite geometric series ...
1
vote
2answers
84 views

Swap two integers in different ways

This is a famous rudimentary problem : how to use mathematical operations (not any other temporary variable or storage) to swap two integers A and B. The most well-known way is the following: ...
-1
votes
1answer
81 views

Computation of integral $\int_{0}^{1}\ln(p)\ln(1-p)p^{2}\,dp$

I want to compute this integral: \begin{equation*} J=\int_{0}^{1}\ln(p)\ln(1-p)p^{2}dp \end{equation*} It will be great if you can detail the proof. I tried to do change of variable it does not ...
1
vote
1answer
59 views

For how many seconds do I need to turn the pedal?

For how many seconds do I need to turn the pedal of a bike, so that the number of turns is equal to the value of my velocity in the given moment measured in km/h.
0
votes
2answers
165 views

How to better compute this eta formula

In the question MRB constant proofs wanted , I gave the following excerpt from http://marvinrayburns.com/UniversalTOC25.pdf . . I accurately worked formula 44 in Matheamatica in the following code. ...
4
votes
0answers
68 views

Finding every $n$ such that $n\times$ ('reverse' number of $n)=m^2$ such as $1584\times 4851={2772}^2$

Let $r(n)$ be the 'reverse' number of $n$ in the decimal system. For example, $r(1234)=4321$. Then, here is my question. Question : Can we find every $n(\in\mathbb N)$, which is not a square ...
2
votes
1answer
189 views

Monotonically increasing path in a complete graph

Given a complete graph with n vertices such that all edge weights are distinct. Prove that we can find a monotonically increasing path of length n-1. I tried finding such a path by sorting the edges ...
1
vote
0answers
30 views

Converting dot producto to set of arithmetic mean differences?

Ok so I am reading a book on linear algebra ( Gilbert Strang to be specific) and I am on second problem set, challenge problem, problem 29. In solutions it appears that the author states that: ...
2
votes
1answer
544 views

roulette wheel sequence

Is the sequence of numbers around a European roulette wheel (the integers from 0 to 36 inclusive) random or is there a pattern to it? It is said to have been devised by Pascal, which might be thought ...
1
vote
0answers
72 views

Net for both cube and regular tetrahedron

At how to fold it by Joseph O'Rourke, there is a net given that can be folded into a cube or irregular tetrahedron. Is there a net that can be folded into either a cube or regular tetrahedron?
3
votes
0answers
471 views

Guilloché security printing — can it be cracked?

Money uses Security printing, and often uses Guilloché patterns. These curves are inscribed by wheels on wheels on wheels, ten wheels deep in some cases. For example, the back of the US $1 bill has ...
4
votes
2answers
698 views

Expected number of points on circle to form an acute angled triangle

This problem was asked to me in an interview. We keep on adding points on a circle uniformly until there exist three points on the circle which form an acute angled triangle. What is the expected ...
5
votes
2answers
3k views

Can you divide a square into 5 equal area regions

Given this shape: Is it possible to divide the cyan area into 5 equal area shapes such that: Each shape is the same Each shape has an edge touching the red square Each shape has an edge touching ...
2
votes
0answers
748 views

K non-intersecting diagonals in a polygon

Given a regular N-sided polygon, how many ways can you draw K non-intersecting diagonals? Any pair of diagonals must not intersect strictly inside the polygon. For e.g. N = 4 and K = 2 -> 2 ways ...
2
votes
1answer
59 views

What points do have three points with minimal distance on $x^2$?

Suppose you have a function $f: \mathbb{R} \rightarrow \mathbb{R}$ and a Point $P = (x,y) \in \mathbb{R}^2$. Now you want to find all $x_1, \dots, x_n$ such that $$\forall \tilde x \in \mathbb{R} ...
3
votes
4answers
865 views

What is the most mathematical flag? [closed]

I know it sounds stupid. But my professor asked us which is the most mathematical flag. As I know most of the flags of the countries are rectangle then what does he mean by most mathematical flag?
5
votes
1answer
102 views

Investigating the density of special integers

I was working on a problem earlier and came up with a solution using the following type of integers: Call an integer $n \geq 3$ convenient if the following hold: $n$ is a squarefree odd integer if ...
0
votes
0answers
127 views

Where to find more of these puzzles?

Examples: A packing company supplies storage boxes in three different sizes: small, medium, and large. All three types of box have the same ratio of width:length and height:length. It is noted ...
6
votes
1answer
456 views

MRB constant proofs wanted

This article has been edited for a bounty. $C$ MRB, the MRB constant, is defined at http://mathworld.wolfram.com/MRBConstant.html . There is an excellent 56 page paper whose author has passed away. ...
2
votes
1answer
114 views

Why these exact values?

In Mathematica I have In[181]:= FullSimplify[ArcSin[10^(1/2)] == (Pi/2 - ArcSinh[3] I)] Out[181]= True In[206]:= FullSimplify[ArcSin[100^(1/3)] == (Pi/2 - ArcCosh[10^(2/3)] I)] Out[206]= True ...
0
votes
3answers
203 views

Coded language puzzle!! [closed]

Here is a puzzle I can't crack. It goes like this: In a certain coded language MANGO=3/5 ORANGE=2/6 APPLE=1/5 Then, POTATO=?? The answer is 5/6. I would like to know to arrive at the answer.
7
votes
1answer
344 views

Why do my professors ignore my work? [closed]

I'm a high-school student finishing in December and about to pursue a career in mathematics. In my free time, I like to ''research'' hard problems and come up with unique proofs or combine ...
2
votes
0answers
82 views

How many Hamiltonian loop are there in a big rectangle?

Suppose I have some big rectangle made of $n \times m$ squares, and I want to place tiles on it in a manner that makes a picture of a hamiltonian loop. I can transform this problem into a problem ...
5
votes
1answer
397 views

Tricky Puzzle!! Please help.

I stumbled upon a puzzle I can't crack. It goes like this: In a certain Code language: 7321=6 5342=3 8645=15 Then 9312=? The Answer is 9. But I can't seem to find the logic behind it??
0
votes
1answer
29 views

What can be the value of $m$ in following equation

During calculations I got this step $$(e^m/((m+1)^{m+1}) )^{3n/4} = 1/2^n$$ I want the value of m here??
6
votes
2answers
258 views

How small is the smallest circle a car can drive?

Lets say we have a model of a car with two fixed back wheels and two wheels in front that steer in the same angle: The wheelbase $w$ is the fixed distance of the two wheel axes. $\alpha_m$ is the ...
5
votes
0answers
387 views

Paul Erdős Joke.

I was watching the great documentary "$N$ is a Number" and in it Erdős tells a joke where he writes: PGOM LD AD LD CD Which means poor great old man, living dead, archeological discovery, legally ...
1
vote
1answer
81 views

Finding the time taken by a flight

I came across a question today which is as follows: A Flight takes off at 2 A.M from northeast direction and travels for 11 hours to reach the destination, which is in northwest direction. Given ...
0
votes
1answer
662 views

Among these figures circle, square, rectangle, isosceles triangle which has the greatest perimeter had the same area?

Among these figures circle, square, rectangle, isosceles triangle which has the greatest perimeter had the same area geometrically ?
2
votes
1answer
92 views

Throw dice, what does this mathematical expression mean in real life?

Assuming we have a dice and the event that if we throw dice for the k-th time and get a 6 is given by $A_k$, is there an actual explanation what $A:= \cap_{i=1}^{\infty} \cup_{j=i}^{\infty} A_j$ is?
2
votes
1answer
127 views

Weird system of equations

X : 2 = 7 Y : 2 = 6 X + Y = 15 Find X and Y. I think maybe this is some unpositional number system. I've tried positional, and it works for basis 21 (if we take X=D, and Y=C), but professor told me ...
1
vote
1answer
123 views

Radius ratio for four packed circles

Suppose we are given four circles $A,B,C,D$ in the Euclidean plane having radii $r_A,r_B,r_C,r_D$ such that $r_A=r_C,r_B=r_D$ and circles $A,C$ are tangent to each other and to $B,D$ but $B,D$ are ...
3
votes
1answer
130 views

Calculating the number of triangles

I am trying to calculate how many triangles that can be found in an equilateral triangle with $2n$ lines starting at the bottom angles and ending at the opposite side, such that equally many lines ...
3
votes
3answers
117 views

Don't understand this problem: There are only 2 pairs of positive integers $(x,y)$ for which…

..both $\frac{21}{x}$ and $\frac{70}{y}$ are in lowest terms and for which $\frac{21}{x} + \frac{70}{y}$ is an integer. One such pair is $(1,1)$. What is the other such pair? This is a Mathematics ...
4
votes
0answers
174 views

Can we get a 'good' approximate value of $\sqrt 2$ by an equation which uses each of $1,2,\cdots,9$ once such as $12653\div 8947\approx1.414217$?

I've been interested in representing $\sqrt 2\approx 1.414213562373095$ by an equation which uses each of $1,2,\cdots,9$ once. Suppose that the following conditions must be satisfied. Then, can we get ...
5
votes
1answer
213 views

Smullyan-To-Mock-a-Mockingbird, Find egocentric bird in L

Question (29, p. 81). Let me tell you the most surprising thing I know about larks: Suppose we are given that the forest contains a lark $L$ and we are not given any other information. From just ...