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

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7
votes
3answers
161 views

Trouble simplifying a tough equation

I'm having trouble simplifying the following equation. I've tried grouping terms in different ways, but it's not looking any more joyful. Can someone please help with its resolution? Hopefully by ...
5
votes
1answer
342 views

How is tessellation defined in Mathematics?

Hi. I am a GCSE student and I am interested in Maths. I read few books on maths and learned some mathematical analysis. I know of convergent series but I would like to know how identical sets(not ...
2
votes
3answers
133 views

Pat the Mathemamagician Part 2

Sal the Magician asks you to pick any five cards from a standard deck. You do so, and then hand them to Sal’s assistant Pat. Then you pick one of the five cards, and Pat puts it back into the deck, ...
3
votes
0answers
137 views

Is there a way to determine how many solution does “ The hundred Fowls problems” have looking at the coefficients?

I was looking at the different versions of the hundred fowls problems. I came across the problem posed by Chinese mathematicians posed in 5th century,and then Indians in 9th, 10th centuries. Alcuin of ...
6
votes
3answers
311 views

Palindrome of numbers from 1-n

A palindrome is a number or word that is the same when read forward and backward, for example, “176671” and “civic.” Can the number obtained by writing the numbers from 1 to n in order (n > 1) be a ...
1
vote
1answer
48 views

How to get range of 1 to 10 by index?

I have a collection of lessons divided by levels Each level has 10 chapters. ...
83
votes
3answers
8k views

Topology: The Board Game

Edit: I've drawn up some different rules, a map and some cards for playing an actual version of the game. They're available at my personal website with a Creative Commons Attribution 4.0 license. ...
1
vote
3answers
599 views

$5n+1$, $3n-1$ problem, smallest repeating cycle and Collatz conjecture

Among the Collatz conjecture we have other "similar" problems that are solved and have repeating cycles. $5n+1$ has the repeating cycle $13, 66, 33, 166, 83, 416, 208, 104, 52, 26$, with a length of ...
5
votes
3answers
234 views

What is the value of D here?

Number $S$ is obtained by squaring the sum of digits of a two digit number $D$. If the difference between $S$ and $D$ is $27$, then the two digit number $D$ is? My thoughts: Let the two digit number ...
1
vote
2answers
250 views

$N \equiv 3 (\textrm{mod } 4)$ and Collatz conjecture

Can the Collatz conjecture also be interpreted as behaviour, transformation of number of form $N\equiv 3(\textrm{mod }4)$ to the form of $N\equiv 1(\textrm{mod }4)$ Because integers of the form ...
2
votes
1answer
248 views

Dissection of a chess board into 4 congruent pieces

Consider a standard $8\times 8$ chessboard where a pawn is placed on each of the squares $d1,d2,d3,d4$ . Dissect the board into $4$ congruent pieces (reflections are allowed) such that each piece ...
3
votes
2answers
62 views

Calculating the most efficient number of group payment transactions required

If you have a group of people who purchase items together and split the costs (not always evenly). How can you calculate the most efficient number of transactions required to settle outstanding debt. ...
0
votes
4answers
400 views

A logic puzzle from TES: Arena

Its nice when games have riddles hidden in them. While playing TES:Arena, I came across an unusual logical puzzle: There are 3 cells. If Cell 3 holds worthless brass, Cell 2 holds the gold key. If ...
18
votes
1answer
409 views

Mathematical Quine

I have recently discovered that I can create letters and any shape I want by hiding parts of curves by making them complex. To generalise if I want $x>a$ then I multiply my function by ...
6
votes
2answers
1k views

Useless math that become useful

I'm writing an article on Lychrel numbers and some people pointed out that this is completely useless. My idea is to amend my article with some theories that seemed useless when they are created but ...
2
votes
1answer
1k views

In how many ways ( using only whole numbers ) can we divide 49 into 6 parts so that we can obtain any number between 1 to 49?

The series which forms the basis of all the other series is:- 1,2,4,8,16,18. Some other combinations are:- 1,2,3,7,14,22 ; 1,2,4,7,15,20 ; 1,2,4,8,13,21. However, I obtained the basic combination by ...
8
votes
2answers
595 views

What is the most unfair set of three nontransitive dice?

In a set nontransitive dice, each die is superior to another die, but is inferior to a third. It is similar to the game of rock-paper-scissors. Here is one example: ...
5
votes
3answers
305 views

How to formally model the “hesitation” in the hat-guessing puzzle?

Hua Luogeng (in Chinese, 华罗庚) took a hat-guessing puzzle as an illustration in a booklet focusing on mathematical induction. The following description is a literal translation from Chinese. ...
20
votes
1answer
1k views

The $n$ Immortals problem.

I saw this riddle posted on reddit a long time ago, called the "Seven Immortals." In the beginning, the world is inhabited by seven immortals, ageless and sexless, who begin to multiply and ...
14
votes
1answer
741 views

“$n$-Yahtzee” question

Suppose that you have $n \geq 1$ standard 6-sided dice. If all the dice display the same number, we call this an $n$-Yahtzee. Follow this algorithm: Roll all the dice. Set aside those dice with ...
3
votes
1answer
137 views

Monty Hall Application

Driver A comes to a 3 way path junction but is not sure which one to take. Just as he decides to take path 1, a cyclist came by and told driver A all he knows is that he is going on path 3 which would ...
3
votes
2answers
367 views

What are good methods for solving Conway's card-stacking puzzle?

Suppose there is a table with three marked spots, $A, B, $ and $C$, on which playing cards can be put, face up. Initially, an ace (1), a deuce (2), and a trey (3) are placed on one or more of these ...
5
votes
1answer
236 views

asymptotics of the square indicator sum for subsequences of digits

Introduce the function $g(n)$ defined for positive integer arguments $n$ as the count of squares of positive integers among the numbers that can be formed by taking some subsequence of the digits of ...
0
votes
1answer
104 views

finding average price of two lots of shares

Sorry, not a math guy, this might be an overly simple question for the lot of you, but it's a calculation that I'll have to do a lot possibly, so please show me the best way to do it. If I have $1265$ ...
0
votes
4answers
135 views

Is there a theorem that disproves this or is this just some made up meaningless thing?

I find this slightly funny. I saw this on a meme:$$\begin{align}a=x\\ a+a=a+x\\ 2a=a+x\\ 2a-2x=a+x-2x\\ 2(a-x)=a+x-2x\\ 2(a-x)=a-x\\ 2=1\end{align}$$ How can these strange algebraic manipulations not ...
2
votes
1answer
450 views

finding nearest perfect square for a fractional number

Is it possible to have a clear definition for the nearest perfect square number for a fractional number? For example, let us consider a number 0.004. What is another decimal number closest to it, that ...
3
votes
3answers
104 views

What is the smallest number which begins with 7 and if you bring the 7 to the least significant position it becomes a third of the original number?

First I wrote the equation: $7\times 10^2+c_1\times10^1+c_0\times10^0 = 3(100c_1+10c_0+7)$ which becomes $679=290c_1+29c_0$ Then I try fix as many variables as possible. In this first iteration, ...
1
vote
2answers
264 views

Is my proof that the medians of a triangle are concurrent valid?

Consider any triangle ABC. Connect the midpoints of each of the three sides. The inscribed triangle is equal to the other three triangles and they are all congruent. It turns out that the medians of ...
7
votes
1answer
331 views

How did Euler solve the 4-whole-numbers-adding-up-to-a-perfect-square problem?

So I was watching a video on Leonhard Euler about how he amazingly solved so many difficult problems and one of the many problems that he solved was this: ...
8
votes
0answers
139 views

Take an m x n grid, and in each box pick two opposite corners at random to connect. What can be said about the resulting pattern?

Inspired by the upcoming book 10 PRINT CHR$(205.5+RND(1)); : GOTO 10 by Nick Montfort et al., whose title derives from this particular example of emergent behavior. Here's an example: (Note that ...
1
vote
1answer
160 views

Linear Algebra Recreational Problem

For each positive integer $k$, find the smallest number $n_k$ for which there exist real $n_k$ by $ n_k$ matrices $A_1; A_2; ....; A_k$ such that all of the following conditions hold: $$ \text{ 1. } ...
2
votes
4answers
393 views

Monty Hall problem vs. roulette systems - how are they different?

So I got interested in the Monty Hall problem - I understand what it's about, but somehow I can't wrap my head around the idea of the final choice not being 50/50. More precisely: we all know (or ...
22
votes
2answers
1k views

Question about a program generating palindromic prime numbers

I'm a programmer and software designer. I'm definitely not a mathematician and my maths is quite basic. One of my colleagues challenged me to generate a palindromic prime number, at least 1000 digits ...
3
votes
2answers
162 views

Men on a boat problem

There is the usual question of some men on a boat- various men have various speeds, the boat has a capacity of 2 men, and the boat takes on the speed of the slowest man in the boat at any given time. ...
0
votes
1answer
113 views

Closest Packing of Spherical Caps

Let the surface $S_n$ of the unit ball in $\mathbb{R}^n$ centered at the origin $O$ be defined as the set of points $P(x_1,x_2,…,x_n )$ such that $x_1^2+x_2^2+⋯+x_n^2=1$. Let the spherical cap $C(α)$ ...
0
votes
1answer
154 views

Recreational mathematics - Digit sum

Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3 Can you help me with this question?
6
votes
0answers
143 views

Card passing game, maximum length

Quoting from this question: There are 25 people sitting around a table and each person has two cards. One of the numbers 1,2,..., 25 is written on each card, and each number occurs on exactly two ...
1
vote
3answers
650 views

Problems like the handshake problem

I am in college and my RA has been putting up little thought problems on his door for us to see as we pass by, but the ones he puts up aren't too interesting. I wrote up the handshake problem (invite ...
2
votes
2answers
116 views

combinations problem about apples and pears

Carlo has six apples and six pears: how many ways he can set in a row 6 fruits so that there should never be a pear between two apples? Thanks in advance to everyone who will help me resolving this ...
8
votes
1answer
210 views

Do roots of a polynomial with coefficients from a Collatz sequence all fall in a disk of radius 1.5?

Consider a modified version of Collatz sequence: $C(n)=\left\{ \begin{array}{ll} \frac{3n+1}{2} & n\ \mathrm{odd} \\ \frac{n}{2}& n\ \mathrm{even}\end{array} \right.$ Let $F_n$ be the ...
6
votes
2answers
268 views

Vector spaces inquiry

Denote By $V$ the real vector spaces of all real polynomials in one variable, and let $P : V \rightarrow \mathbb{R}$ be a linear map. Suppose that $\forall$ $f,g \in V$ with $P(fg) = 0$ we have $P(f) ...
3
votes
2answers
325 views

A less challenging trivia problem

There are 25 people sitting around a table and each person has two cards. One of the numbers 1,2,..., 25 is written on each card, and each number occurs on exactly two cards. At a signal, each person ...
4
votes
2answers
405 views

A book of probability puzzles

I would like to train some recreational probability (Puzzles). Does any of you know a good collection? Preferably with hints or answers. I've been studying quite a bit of probability theory, but I ...
2
votes
1answer
536 views

Puzzle on the triangle.

In triangle top four figures that have to be repositioned to form the "triangle" without a unit square. How to explain this? Thank's.
8
votes
3answers
203 views

Group of sphere transformations, impressing friends

Ok, so here's the story: I am reading a book on algebra and, via some exercises, discovered that in any group $G$, the order of $x \cdot y$, written $o(x \cdot y)$, equals $o(y \cdot x)$. Now, this is ...
0
votes
2answers
200 views

Mathematical doodle games

Vi Hart's doodling videos and a 4 year old son interested in mazes has made me wonder: What are some interesting mathematical "doodling" diversions/games that satisfy the following criteria: 1) They ...
2
votes
2answers
208 views

(Theoretic) probability greater than 1

I am not expecting a "realistic" answer to my question, since it is based on an impossible scenario. What I'm waiting for is a theoretic explanation/interpretation so that I can sleep at night :) ...
1
vote
2answers
188 views

100 roads in a city, 1 is closed

In a certain country, 100 roads lead out of each city, and one can travel along those roads from any city to any other. One road is closed for repairs. Prove that one can still get from any city to ...
5
votes
1answer
314 views

67 67 67 : use 3, 67's use any way how to get 11222

I need to get 11222 using three 67 s (Sixty seven) We can use any operation in any maner 67 67 67 use 3, 67's use any way but to get 11222.
0
votes
2answers
1k views

What is the significance of the mirror numbers?

I'd like to hear insights and theory of the mirror numbers and their possible significance in mathematics and geometry. With mirror numbers I mean these four examples: ...