If ABC and DEF are both 3-digit numbers such that A, B, C, D, E and F are distinct non-zero digits such that…
If ABC and DEF are both 3-digit numbers such that A, B, C, D, E and F are distinct non-zero digits such that ABC + DEF = 1111, then what is the value of A + B + C + D + E + F?
28
29
30
31
Solution
Adding two 3-digit numbers to get 1111. In the units column $C + F$ ends in 1, so $C + F = 11$ (carry 1). In the tens column $B + E + 1$ ends in 1, so $B + E + 1 = 11$, i.e. $B + E = 10$ (carry 1). In the hundreds column $A + D + 1 = 11$, so $A + D = 10$. Total $= (A+D) + (B+E) + (C+F) = 10 + 10 + 11 = 31$.