Each of the positive integers a, b, and c is a three-digit integer. If each of the digits 1 through 9 appears in one of these three integers, what is the maximum possible value of the sum of a, b, and c?
Select: A) 2445 B) 2331 C) 2874 D) 2801 E) 2256
According to the stem we should use the digits 1 through 9 to construct 3 three-digit integers, so that their sum is as big as possible.   To maximize the sum, maximize the hundreds digits of a, b, and c, so make them 9, 8, and 7.   Next, minimize tens digits. Make them 6, 5, and 4.   Use the remaining digits (3, 2, and 1) for units digits.   So, a would be 963, b would be 852 and c would be 741.   741 + 852 + 963 =2256.   Answer: 2256.
<result>E</result>
Each of the positive integers a, b, and c is a three-digit integer. If each of the digits 1 through 9 appears in one of these three integers, what is the maximum possible value of the sum of a, b, and c?