How many solutions in positive integers (0 isn’t positive, of course) of a + b + c + d + e + f = 18 exist? We count 3+ 3+ 3+ 3+ 5+ 1 and 3+ 3+ 3+ 5+ 1+ 3 as distinct solutions. In how many of them all the numbers a, . . . , f are odd, and in how many exactly four of them are even?