Question

有多少个两位数的各位数字和是完全平方数？

How many two-digit numbers have digits whose sum is a perfect square?

$13$

$16$

$17$

$18$

$19$

数位和为 $1$ 的数有 $1$ 个： $10$ 。

数位和为 $4$ 的数有 $4$ 个： $13, 22, 31,$ 和 $40$ 。

数位和为 $9$ 的数有 $9$ 个： $18, 27, 36, 45, 54,$ $63, 72, 81,$ 和 $90$ 。

数位和为 $16$ 的数有 $3$ 个： $79, 88,$ 和 $97$ 。

因此共有 $17$ 个数满足题意。

所以正确答案是 C。

There is $1$ number whose digit sum is $1$ : $10.$

There are $4$ numbers whose digit sum is $4$ : $13, 22, 31,$ and $40.$

There are $9$ numbers whose digit sum is $9$ : $18, 27, 36, 45, 54,$ $63, 72, 81,$ and $90.$

There are $3$ numbers whose digit sum is $16$ : $79, 88,$ and $97.$

Therefore, there are $17$ numbers that satisfy the problem statement.

Thus, C is the correct answer.