Question 18
Let $n \gt 2$ be an even integer. Tokens must be placed on the cells of an $n \times n$ board so that in each column the number of tokens is even and nonzero, and in each row the number of tokens is odd.
Determine the smallest number of tokens that must be placed on the board to satisfy this rule.
Show a configuration with that number of tokens and explain why the rule cannot be satisfied with fewer tokens.
Determine the smallest number of tokens that must be placed on the board to satisfy this rule.
Show a configuration with that number of tokens and explain why the rule cannot be satisfied with fewer tokens.