Final answer:
The least possible sum of six different digits used in an addition problem, without repeating any, is the sum of the first six unique digits 0-5, excluding the use of 0 at the beginning of a number. By strategically placing 1, 2, 3, 4, and 5 in the most significant digit places and the 0 in the least, the least sum of 15 is achieved.
Step-by-step explanation:
To find the least possible sum of six different digits in an addition problem, we look for the lowest digits that can be used without repeating any. From the smallest to the largest, the first six unique single digits are 0, 1, 2, 3, 4, and 5. However, we cannot use 0 as the first digit of a number. If Raquel is filling in blanks for an addition problem, the lowest possible sum would mean using the numbers 1, 2, 3, 4, and 5 across her six blanks, with 0 being the last digit, as it cannot lead a number. Let's assume the addition problem looks something like '__ + __ = __'.
To minimize the sum, Raquel would want to make the smallest possible two-digit numbers. This would be done by placing '1' and '2' in the hundreds and tens place of the first number, '3' and '4' in the hundreds and tens place of the second number, and '5' and '0' for the hundred and tens place of the sum.
Therefore, the least possible sum is achieved by putting the smallest numbers in the most significant digit places and the largest numbers in the least significant places. The least possible sum of the six digits used in the correct additions statement is 1 + 2 + 3 + 4 + 5 + 0 = 15.