## Online Calcualte Politeness of Number

Calculate politeness of a number online, i.e., the number of ways it can be expressed as the sum of consecutive integers.

## Online Calculate Sum of Proper Divisors

Online tool for prime factorization and calculating sum of proper divisors. The algorithm is implemented in JavaScript and UI in Vue.js.

## Online Prime Factorization

Online tool that helps you do prime factorization. The algorithm is implemented in JavaScript and UI in Vue.js.

## Descartes' rules of signs

Hard to believe that I don't remember seeing Descartes' rules of signs before -- you'd think this is impossible given the time I spent on ...

## Helly's theorem

This is the last of a small series of similar and basic results in convex geometry.

## Caratheodory's theorem

Previous I used Caratheodory's theorem to prove Radon's theorem, now I'm going to prove the former.

I came across Radon's theorem the other day, and found this proof. It must have been discovered before.

## Balancing numbers

There are 2n+1 coins each associated with a weight. When we remove any coin, we can split the rest into two piles each with n coins...

## Numbers game

Given a sequence of (n) integers (a_1,ldots,a_n), we map it to ...

## No crossing!

On the 2D plane there are (n) blue and (n) red points, no three of them are co-linear. Then we can always pair a blue point with a red ...

## Maximum number of pairwise non-acute vectors in R^n

It is said to be well-known, but perhaps I've never seen it before:

## 2017 APMO Problem 3

Let (A(n)) denote the number of sequences (a_1ge a_2gecdots{}ge a_k) of positive integers for which (a_1+cdots+a_k = n) and each ...

## APMO 2017 Problem 1

We call a (5)-tuple of integers arrangeable if its elements can be labeled (a, b, c, d, e) in some order so that (a-b+c-d+e=29). Deter...

## 2009 USAMO Problem 3

I found a different solution to the second part of this problem. We define a chessboard polygon to be a polygon whose edges are situate...

## USAMO 2017 Problem 2

Let (m_1, m_2, ldots, m_n) be a collection of (n) positive integers, not necessarily distinct. For any sequence of integers (A = (a_1...

## USAMO 2008 Problem 3

The problem is rephrased. Q: A diamond of size n consists of 2n rows of nodes with lengths from top to bottom being 1, 3, 5, ..., 2n-1...

## USAMO 2017 Problem 4

Let (P_1, P_2, dots, P_{2n}) be (2n) distinct points on the unit circle (x^2+y^2=1), other than ((1,0)). Each point is colored eit...

## IMO 2007 Problem 3

In a mathematical competition some competitors are friends. Friendship is always mutual. Call a group of competitors a clique if each two of...

## IMO 2016 Problem 6

There are n>=2 line segments in the plane such that every two segments cross and no three segments meet at a point. Geoff has to choose an ...