SOLUTION: Each letter "D" "N" and "A" in this addition: DNA+DAN=AND ,represents a different digit. What is the sum of D + N + A?

Question 382749: Each letter "D" "N" and "A" in this addition: DNA+DAN=AND ,represents a different digit. What is the sum of D + N + A?

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
We have
(100D + 10N + A) + (100D + 10A + N) = 100A + 10N + D
200D + 11N + 11A = 100A + 10N + D
199D + N = 89A
Suppose we write the last expression modulo 89 to obtain
21D + N = 0 = 89 = 178 etc. (modulo 89)
21D + N cannot be 178 because D would become larger than 5 (which would give a 4-digit sum). Therefore 21D + N = 89 --> D = 4, N = 5.
Solving, we have
796 + 5 = 89A --> 801 = 89A --> A = 9
Therefore D + N + A = 18.
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