Each of the positive integers a, b, and c is a three-digit integer. If each of the digits 0 through 8 appears in one of these three integers, what is the minimum possible value of the sum of a, b, and c?  Choose the correct choice from the following choices:
A) 45
B) 666
C) 711
D) 801
E) 1368
According to the stem we should use the digits 0 through 7 to construct 3 three-digit integers, so that their sum is as small as possible.   To minimize the sum, minimize the hundreds digits of a, b, and c, so make them 1, 2, and 3.   Next, minimize tens digits. Make them 0, 4, and 5.   Use the remaining digits (6, 7, and 8) for units digits.   So, a would be 106, b would be 247 and c would be 358.   106 + 247 + 358= 
<gadget id="calculator">106 + 247 + 358</gadget>
<output>711</output>
711.   Answer: 711.
<result>C</result>
Each of the positive integers a, b, and c is a three-digit integer. If each of the digits 0 through 8 appears in one of these three integers, what is the minimum possible value of the sum of a, b, and c?