1. The problem statement, all variables and given/known data Find the number of solutions to the equation x + y + z + t = 16, where x, y, z, and t are: i) odd integers ii) even integers 2. Relevant equations N/A 3. The attempt at a solution I know the total number of solutions is 19 choose 3. So I'm thinking I can obtain the answer for i) by subtracting the universal set by the set where at least one of the variables is an even integer. I cannot figure out how to calculate the number of solutions where at least one variable is even.