Question

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 $S?$

$\ 1$

$\ 4$

$\ 5$

$\ 15$

$\ 21$

Solution:

The smallest possible sum of two three-digit numbers with six distinct digits is at least $104+235=339$ . Any three-digit number at least $339$ with digit sum less than $4$ would have to be one of $100,101,110,200,201,210,300,301,310$ , all of which are less than $339$ . So the digit sum of $S$ is at least $4$ .

The example $157+243=400$ uses six distinct digits and has digit sum $4$ . Thus the smallest possible digit sum is $4$ .

Thus, the correct answer is B.

2016 AMC 10B Problem 6

Solution:

Problem 6 in Other Years