Question

在所示加法算式中，每个数字都被一个字母代替。若不同字母表示不同数字，那么 $C =$

$\begin{array}{cccc} & A & B & C \\ & & A & B \\ + & & & A \\ \hline & 3 & 0 & 0 \end{array}$

In the addition problem shown, each digit has been replaced by a letter. If different letters represent different digits, then $C =$

$\begin{array}{cccc} & A & B & C \\ & & A & B \\ + & & & A \\ \hline & 3 & 0 & 0 \end{array}$

$1$

$3$

$5$

$7$

$9$

三个数相加为 $111A + 11B + C = 300$ 。若 $A = 1$ ，数值太小；若 $A \ge 3$ ，数值太大，所以 $A = 2$ 。

此时 $11B + C = 78$ ，只能有 $B = 7$ 且 $C = 1$ 。所以 $C = 1$ 。

所以正确答案是 A。

The three numbers add to $111A + 11B + C = 300.$ Since $A = 1$ is too small and $A \ge 3$ is too large, $A = 2.$

Then $11B + C = 78,$ which forces $B = 7$ and $C = 1.$ So $C = 1.$

Thus, the correct answer is A .