Question

在下面的加法中， $A$ 和 $B$ 是非零数字：

$\begin{array}{r} 9876 \\ A32 \\ +B1 \\ \hline \end{array}$

这三个整数的和有多少位数字（数字不一定互不相同）？

In the addition problem below, $A$ and $B$ are nonzero digits:

$\begin{array}{r} 9876 \\ A32 \\ +B1 \\ \hline \end{array}$

How many digits (not necessarily different) are in the sum of the three whole numbers?

$4$

$5$

$6$

$9$

取决于 $A$ 和 $B$ 的值

depends on the values of $A$ and $B$

$9876$ 已经很接近 $10{,}000$ ，所以再加任何正数都会超过它

The number $9876$ is already close to $10{,}000,$ so adding anything pushes the sum past it

也检查最大可能和，取 $A = B = 9$

Check the largest possible sum too, using $A = B = 9$

因为 $A$ 和 $B$ 至少为 $1$ ，所以和至少是 $9876 + 132 + 11 = 10{,}019$ ，有 $5$ 位。

另一端，当 $A = B = 9$ 时，和为 $9876 + 932 + 91 = 10{,}899$ ，仍然是 $5$ 位。因此和总是恰好有 $5$ 位。

所以正确答案是 B。

Since $A$ and $B$ are at least $1,$ the sum is at least $9876 + 132 + 11 = 10{,}019,$ which has $5$ digits.

At the other extreme, with $A = B = 9$ the sum is $9876 + 932 + 91 = 10{,}899,$ still $5$ digits. So the sum always has exactly $5$ digits.

Thus, the correct answer is B .