AMC10 2016 B

AMC10 2016 B · Q6

AMC10 2016 B · Q6. It mainly tests Money / coins, Casework.

Laura added two three-digit positive integers. All six digits in these numbers are different. Laura's sum is a three-digit number $S$. What is the smallest possible value for the sum of the digits of $S$?

劳拉把两个三位正整数相加。这两个数的六个数字都互不相同。劳拉得到的和是一个三位数 $S$。求 $S$ 的各位数字之和的最小可能值。

(A) 1 1

(B) 4 4

(D) 15 15

(E) 21 21

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): Because $S$ has to be greater than 300, the digit sum has to be at least 4, and an example like $197 + 203 = 400$ shows that 4 is indeed the smallest possible value.

答案（B）：因为 $S$ 必须大于 300，数字和至少为 4，而例如 $197 + 203 = 400$ 这样的例子表明 4 确实是可能的最小值。

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