Knowing Your A, B and C
Number Theory
Level
2
\begin{array} { l l l l l } & & A & B & C \\+ && A & B & C \\+ && A & B & C \\ & \hline & \\ &&\ B & B & B \end{array}
What is
The answer is 13.
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1 solution
The question can be rewritten as 3 0 0 A + 3 0 B + 3 C = 1 1 1 B .
If we simplify the equation, you get 1 0 0 A + C = 2 7 B .
That equation can be rewritten as 2 5 B − 1 0 0 A + 2 B = C .
For now, we want A, B, and C to be as small as possible. Because 2 B is a negligible amount as long as B < 5 , we can ignore it for now.
Now, we should make 2 5 B − 1 0 0 A = 0 . This is achieved by setting A to 1 and B to 4.
This leaves us with 2 ⋅ 4 = C , or C = 8 .
1 + 4 + 8 = 1 3 , so the answer is 13.