MathDB

A5

Part of 2018 Malaysia National Olympiad

Problems(3)

OMK 2018 Sulong, Section A Problem 5

Source: OMK 2018 Sulong, Section A Problem 5

6/21/2021
Determine the value of (101×99)(101 \times 99) - (102×98)(102 \times 98) + (103×97)(103 \times 97) − (104×96)(104 \times 96) + ... ... + (149×51)(149 \times 51) − (150×50)(150 \times 50).
number theorycontestsPerfect Squaresdifference of squares
no of coloring some faces of a cube 2018 Malaysia OMK Intermediate A5

Source:

9/19/2021
Daud want to paint some faces of a cube with green paint. At least one face must be painted. How many ways are there for him to paint the cube?
Note: Two colorings are considered the same if one can be obtained from the other by rotation.
combinatoricsColoringcube
n^2 - [\sqrt{n} ]= 2018 2018 Malaysia OMK Juniors A5

Source:

9/19/2021
Find the positive integer nn that satisfi es the equation n2−⌊n⌋=2018n^2 - \lfloor \sqrt{n} \rfloor = 2018
floor functionalgebra