# Tagged Questions

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

181 views

2k views

### Rubik's Cube Not a Group?

I read online that although the 3x3x3 is a great example of a mathematical group, larger cubes aren't groups at all. How can that be true? There is obviously an identity and it is closed, so ...
44 views

64 views

### Find the Smallest Value

Find the smallest value of $$a + \frac {1}{(a-b)b}$$ where a>b>0 I found this question in AM-GM inequality problems but I am stuck at this
2k views

### Concrete Mathematics - Towers of Hanoi Recurrence Relation

I've decided to dive in Concrete Mathematics despite only doing a couple of years of undergraduate maths many years ago. I'm looking to work through all the material whilst plugging gaps in my ...
1k views

### Concrete Mathematics - The Josephus Problem

I've been going through Concrete Mathematics and have a question on the inductive proof for the Josephus problem. Recurrent relation: $J(1) = 1$ $J(2n) = 2J(n) - 1$ $J(2n+1) = 2J(n) + 1$...
69 views

36 views

### Given $x^m=y^m ; so \; x=y \;or\; -y$ when m is even. Now $2^0 = 3^0 \; but \; 2 \neq 3$ . How to reason mathematically

The question may sound silly but is there a simple logic to counter the paradox.I will be glad to know if there is. Thank You. Edit: x,y $\in R\;\; x,y \neq 0$, m is a integer. Now x = y when m is ...
42 views

### Edge-matching icosahedron puzzle

Color the edges of an icosahedron with 4 colors so that all 20 triangles have a distinct set of colors. Color the edges of an icosahedron with 6 colors so that all 20 triangles have a distinct set ...
11k views

### Mental Calculations

This is the famous picture "Mental Arithmetic. In the Public School of S. Rachinsky." by the Russian artist Nikolay Bogdanov-Belsky. The problem presented on a blackboard requires computing the ...
759 views

### Sudoku with special properties

Sudoku is a puzzle, with the objective is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 sub-grids that compose the grid (also "sudoku-blocks") contains all of ...
25 views

### Translate thinking into a equation. Finding the lesser value

First of all, bear with me if I name things wrong as I'm null at math. For the same reason please add explanation for dummies in common language if you add an answer with math notation :D I'm trying ...
8 views

### Simple Composite of Relations

My lecturer has given this simple composite of relations question; R = {(1,2), (3,4), (2,1)} S = {(2, 1), (5, 3)} R o S = {(1, 1)} is the answer i acquire. he acquires the answer R o S = {(2,2), (5, ...
27 views

### How to Solve a Function Given Some of its Solutions

Suppose you have a function that defines a series. And suppose you know Some (not all) of the elements of that series. For example, you know your function is n/J, where n is for all positive integers ...
30 views

### Which vertex-transitive planar graphs represent non-self-intersecting polyhedra?

Consider an infinite planar graph with the following properties. Its vertices all have valence $3$. The faces all have $5$ edges. Now put it in cartesian space and require that the faces are all ...
158 views

### The Hardest Sudoku Puzzle

I was playing a casual game of Sudoku today when a friend came by and asked "What's the hardest game of Sudoku possible?" My response: "A Sudoku puzzle with the minimal amount of starting numbers ...
113 views

199 views

### Bicycle Route Optimization Puzzle

I tried to make some expressions about where each person stops the bike, but I couldn't solve it :( There are three people who would like to cross the road. It takes $a$ minutes for the first person ...
118 views

### Intuitive ways to get formula of binomial-like sum

Is there an intuitive way, though I am not sure how to find a conceptual proof either, to establish the following identity: $$\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$$ for all natural ...
40 views

### Making ease-out-bounce formula have a linear start

I'm using a bounce ease out formula, the code for it: https://github.com/jesusgollonet/processing-penner-easing/blob/master/src/Bounce.java#L9. The function is copied here: ...
21 views

### Create a formula to compare different exchange rates (one with a fee)

While looking at exchange rates for an upcoming vacation, I decided to brush up on some old math but wanted to make sure I was thinking about it correctly. $B_1$ charges a rate for USD to EUR ...
2k views

### Are there an infinite set of sets that only have one element in common with each other?

In a card game called Dobble, there are 55 cards, each containing 8 symbols. For each group of two cards, there is only one symbol in common. (The goal of the game being to spot it faster than the ...
152 views

### Recreational problems in set theory?

Most areas of maths that I can think of have a number of fun, recreational problems that come under their category. Nothing deep: number theoretic stuff in olympiads, integrals, limits, products, ...
184 views

41 views

### vector of eigenvalues is an eigenvector

When is it the case that the vector $\begin{bmatrix} \lambda_1 \\ \lambda_2 \\ ... \end{bmatrix}$ of eigenvalues of a matrix is in fact an eigenvector of that matrix?
Suppose a trek begins and on this trek the road is paved by squares with labels on them. The warning sign next to the beginning of the first square, labeled $1$, states: Beware that due to natural ...