Problem

Source: Paraguayan Mathematical Olympiad 2012

Tags: combinatorics proposed, combinatorics



The traveler ant is walking over several chess boards. He only walks vertically and horizontally through the squares of the boards and does not pass two or more times over the same square of a board. a) In a $4$x$4$ board, from which squares can he begin his travel so that he can pass through all the squares of the board? b) In a $5$x$5$ board, from which squares can he begin his travel so that he can pass through all the squares of the board? c) In a $n$x$n$ board, from which squares can he begin his travel so that he can pass through all the squares of the board?