MathDB
Splitting 100x100 table into rectangles

Source: 239 2019 S2

July 31, 2020
geometryrectangle

Problem Statement

Several cells are marked in a 100×100100 \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 kk rectangles containing less than two cells. What is the smallest kk such that Vasya will certainly be able to do this?