Problem

Source: 2019 Junior Balkan MO

Tags: combinatorics, Junior, Balkan, JBMO, 2019



A $5 \times 100$ table is divided into $500$ unit square cells, where $n$ of them are coloured black and the rest are coloured white. Two unit square cells are called adjacent if they share a common side. Each of the unit square cells has at most two adjacent black unit square cells. Find the largest possible value of $n$.