There are 27 different three-digit integers that can be formed using only the digits 1, 2 and 3. If all 27 of the integers were listed, what would their sum be?  Choose the correct choice from the following answers
A) 2,704 B) 2,990 C) 5,404 D) 5,444 E) 5,994
Probably the easiest and fastest way to answer this problem is to think about the average three digit number you can create using just the digits 1,2,3, and to multiply this average number with 27.   The average three digit number is 222 (choosing an average of 1,2,3 for every single digit of the number). So  222*27= 
<gadget id="calculator"> 222*27</gadget>
<output>5_994</output>
5994.   Hence, solution 2,704 is correct.
<result>A</result>
There are 27 different three-digit integers that can be formed using only the digits 1, 2 and 3. If all 27 of the integers were listed, what would their sum be?