Problem 2 of First round - Chessboard and lines
Source: VII International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade
August 29, 2019
combinatoricsChessboard
Problem Statement
A cell is cut from a chessboard , after which an open broken line was built, which vertices are the centers of the remaining cells. Each segment of the broken line has a length or . When is the number of such broken lines bigger – when the cut cell is or ? (The rows and columns on the board are numerated consecutively from 1 to 8.)