MathDB

6

Part of 2015 South East Mathematical Olympiad

Problems(2)

Smallest halving cevian

Source: China Southeast Math Olympiad 2015 Day 2 P6

6/6/2017
In △ABC\triangle ABC, we have three edges with lengths BC=a, CA=b AB=cBC=a, \, CA=b \, AB=c, and c<b<a<2cc<b<a<2c. PP and QQ are two points of the edges of △ABC\triangle ABC, and the straight line PQPQ divides △ABC\triangle ABC into two parts with the same area. Find the minimum value of the length of the line segment PQPQ.
geometry
2015 China South East MO Grade 11 P6

Source: 2015 China South East MO Grade 11 P6

1/16/2018
Given a positive integer n≥2n\geq 2. Let A={(a,b)∣a,b∈{1,2,…,n}}A=\{ (a,b)\mid a,b\in \{ 1,2,…,n\} \} be the set of points in Cartesian coordinate plane. How many ways to colour points in AA, each by one of three fixed colour, such that, for any a,b∈{1,2,…,n−1}a,b\in \{ 1,2,…,n-1\}, if (a,b)(a,b) and (a+1,b)(a+1,b) have same colour, then (a,b+1)(a,b+1) and (a+1,b+1)(a+1,b+1) also have same colour.
combinatorics