Two ants crawl along the sides of the $49$ squares of a $7 * 7$ board. Each ant passes through all $64$ vertices exactly once and returns to its starting point. What is the smallest possible number of sides covered by both ants?
Source: Tournament of towns
Tags: combinatorics
Two ants crawl along the sides of the $49$ squares of a $7 * 7$ board. Each ant passes through all $64$ vertices exactly once and returns to its starting point. What is the smallest possible number of sides covered by both ants?