2

Part of 2019 239 Open Mathematical Olympiad

Problems(2)

Splitting 100x100 table into rectangles

Source: 239 2019 S2

Several cells are marked in a

100 \times 100

table. Vasya wants to split the square into several rectangles such that each rectangle does not contain more than two marked cells and there are at most

k

rectangles containing less than two cells. What is the smallest

k

such that Vasya will certainly be able to do this?

geometryrectangle

Consecutive numbers with 900 divisors

Source: 239 2019 J2

Is it true that there are

130

consecutive natural numbers, such that each of them has exactly

900

natural divisors?

number theoryDivisorsnumber of divisors