$a)$ Is it possible, on modified chessboard $20 \times 30$, to draw a line which cuts exactly $50$ cells where chessboard cells are squares $1 \times 1$ $b)$ What is the maximum number of cells which line can cut on chessboard $m \times n$, $m,n \in \mathbb{N}$
Problem
Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2013
Tags: combinatorics, Chessboard