Question 618975
Consider this in terms of modulo 3. n+4 is equivalent to n+1 (mod 3), so we have to show that out of n, n+2, n+1, only one of them is divisible by 3. Here, it's just simple casework based on n ≡ 0, 1, 2 (mod 3). There will always be exactly one integer of those three that is divisible by 3.