MathDB

A3

Part of 2018 Malaysia National Olympiad

Problems(3)

OMK 2018 Sulong, Section A Problem 3

Source: OMK 2018 Sulong, Section A Problem 3

6/21/2021
Given a regular polygon with nn sides. It is known that there are 12001200 ways to choose three of the vertices of the polygon such that they form the vertices of a right triangle. What is the value of nn?
combinatoricspolygon
4 out of 15 points, vertices of equilateral 2018 Malaysia OMK Intermediate A3

Source:

9/19/2021
On each side of a triangle, 55 points are chosen (other than the vertices of the triangle) and these 1515 points are colored red. How many ways are there to choose four red points such that they form the vertices of a quadrilateral?
combinatoricscombinatorial geometry
buying apples, mangos and papayas 2018 Malaysia OMK Juniors A3

Source:

9/19/2021
Danial went to a fruit stall that sells apples, mangoes, and papayas. Each apple costs 33 RM ,each mango costs 44 RM , and each papaya costs 55 RM . He bought at least one of each fruit, and paid exactly 5050 RM. What is the maximum number of fruits that he could have bought?
algebra