Every 2 digit number is greater than 9 and less than 100 Let M and N be two two-digit numbers, then 9 < M < 100 9 < N < 100 We add those two inequalities term by term: 9 < M < 100 9 < N < 100 ------------ 18 < M+N < 200 So their sum is always greater than 18 and less than 200, so their sum can never be a 4 digit number. That's because 4-digit numbers are all greater than 999. Edwin