# Questions tagged [recreational-mathematics]

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

3,399 questions
Filter by
Sorted by
Tagged with
0answers
81 views

### Find the missing number: $3+5+7=152181$, $4+5+6=202461$, $3+4+7=122172$, $9+4+5=364518$, $8+6+8=?$ [on hold]

Given \begin{align} 3+5+7&=152181 \\ 4+5+6&=202461 \\ 3+4+7&=122172 \\ 9+4+5&=364518 \\ 8+6+8&=\;? \end{align} I am able to get the first two numbers but for third ...
2answers
75 views

### What is the geometry of points inside a square, that are equally distant from the square [on hold]

Image: A visual of the problem For the square ABCD, what would be the geometry of points that are equally distant (distance r) from all points of the square? How would the shape written out by r ...
0answers
95 views

### Smallest number not expressible using first $n$ powers of $2$ (exactly once each), with $+$, $-$, $\times$, $\div$, and parentheses?

Motivation Solution to this problem is a lower bound for a more general problem. Problem Given first $n$ powers of two: $1,2,4,8,16,\dots,2^{n-1}$ that all need to be used exactly once per number ...
1answer
75 views

### Swedish mathematical competition problem for pre-tertiary students

In a class of students, one student is given a bag of 2014 coins whilst none of the other students in the class recieve any coins at all. Every time two students meet, if they have an even amount of ...
1answer
52 views

### Constructing a point arbitrary close to the Mandelbrot set

This question is motivated by the coloring schemes of the Mandelbrot fractal, namely that the color is determined by the points outside the set, and is proportional to the number of iterations $n_c$ ...
0answers
35 views

### Why does the square root of -1 squared have two answers? [duplicate]

If $$(\sqrt{-1})^2 =$$ $$(\sqrt{-1})(\sqrt{-1}) =$$ $$\sqrt{(-1)^2} =$$ $$\sqrt{1} =$$ $$1$$ Does 1 = -1? What is wrong?
1answer
42 views

### Vanishing cuboid problem

Consider 28 $19\times44\times29$ cuboids in a box. {19, 44, 29} {7, 2, 2} pack in a {133, 88, 58} box. {44, 29, 19} {3, 3, 3} pack in a {132, 87, 57} box. By reorienting the cuboids, one can be ...
6answers
215 views

### A curiosity on a first three natural numbers

Let's review a triple of numbers, $1, 2, 3$, it is a curiosity that $$1+2+3 = 1\times2\times3 = 6$$ Are there another triples (or not necessary triples) such that their multiple equal to their sum? ...
0answers
671 views
+100

2answers
54 views

1answer
420 views

### Interesting patterns in $f(k,n)=k\pi-\sum\limits_{x=1}^n\tan^{-1}\left(\frac1{\sqrt[k]x}\right)$

Motivation: If we draw a right-angled triangle $A_1$ with sides $1,1$ then the hypotenuse is of length $\sqrt2$. If we draw a right-angled triangle $A_2$ with sides $\sqrt2,1$ attached to $A_1$ then ...
1answer
75 views

### Spectacular approximation to $\sum_{k=1}^n \{k \log_2 3\}$ where the curly brackets represent the fractional part

As many of the questions that I have asked recently, this is related to my investigations in finding a standard mathematical constant that has 50% of its binary digits equal to zero. My approximation ...
1answer
97 views

### How to prove: $11=10^{12}+10^{7}-45\sum_{n=1}^{999}\csc^4\frac{n\pi}{1000}$ [closed]

How to prove: \begin{equation} 11=10^{12}+10^{7}-45\sum_{n=1}^{999}\csc^4\frac{n\pi}{1000}\;. \end{equation} This identity appears on my clock:
1answer
72 views

### Arbitrarily long palindromes in two consecutive number bases

Is it possible to construct an arbitrarily long double palindrome? The double palindrome of length $d$ is a number that is palindromic (digits are the same when reversed) in two consecutive ...
1answer
77 views

4answers
319 views

### Please let me know why 2/16 has a remainder of 2. Thanks [closed]

I would like to know why this division 2/16 has a remainder of 2. I understand remainders from this division 10/6 = 1 remainder is 4. But I can't figure out why 2/16 has a remainder of 2. Thanks
0answers
62 views

### What is the minimal area of a fully-fledged Dyson sphere?

A Dyson sphere is a hypothetical megastructure made up of a finite number of thin sun-screens in free-fall orbit around a central star. The goal is to harvest as much of the sun's radiation power as ...
1answer
47 views

### How is the quadratic equation formed?

Recently I was going through a problem. Below is the problem. Each evening after the dinner the SIS's students gather together to play the game of Sport Mafia.For the tournament, Alya puts candies ...
0answers
45 views

### Infinite volume but finite surface area, in higher dimensions?

In Infinite Volume but Finite Surface Area a question is asked whether there is some shape in $\Bbb R^3$ that have an infinite volume, but a finite surface area, sort of the opposite of Gabriel's Horn....
0answers
45 views

### Having trouble understanding how symmetry is used in the triomino problem

Given below is the classic combinatoral geometric problem of whether 8x8 board can be covered by 21 straight triominos. It is taken from Solomon W. Golombs Polyminoes and Puzzles. Now I am having ...
1answer
65 views

### Full Change Graphs

The following graph has vertices with total 183. There are 183 ways to remove a set of one of more connected vertices so that the remaining vertices are connected. These 183 sets have distinct ...
0answers
39 views

### Expected number of calls for a Bingo win

I have read a few similar questions (see this question and this one), but cannot figure out how to adapt the solutions to fit my question. Unfortunately, my understanding of math is extremely limited, ...
1answer
102 views

### Simplest Turing Machine for a particular binary string

At the Bank of England is a proposed £50 note. Alan Turing was born on the 23rd June 1912. 23061912 in decimal is 1010111111110010110011000. Starting from a blank tape, what is the simplest Turing ...
1answer
28 views

### What can be a function that take integers as input values,and give output as odd Numbers?

I want a function that can get input as integers and give result as odd numbers. for example if x=1,y=1 then (2,3) (3,5) (4,7) (5,9) (6,11) expressing y in terms of x.
1answer
71 views

### Is the coin fair

So, I told my friend a story ... Probability professor assigned a homework to his students. The assignment was to record a 200 tosses of the fair coin. After the assignments were handed, the ...
1answer
190 views

### A magician places $n$ coins on a table and walks down off the stage.

A magician places n coins on a table and walks down off the stage. A volunteer comes, turns over whichever coins he wishes, selects one coin and whispers its number to the apprentice. Then the ...
2answers
50 views

### An idealized $\infty$-body problem: is an infinite and regular configuration of massive objects stable?

Suppose I have an infinite amount of massive point shaped objects, and I arrange the objects by putting one object on each point of $\mathbb{Z}^2$ within $\mathbb{R}^2$. By symmetry, the gravity ...