Problem (Combinatorics):
The Local Area Inspirational Math Exam comprises 15 questions. All answers are integers ranging from 000 to 999, inclusive. If the 15 answers form an arithmetic progression with the largest possible difference, compute the largest possible sum of those 15 answers.

Solution:
Let $a$ represent the middle $\left(8^{\text {th }}\right)$ term of the sequence, and let $d$ be the difference. Then the terms of the sequence are $a-7 d, a-6 d, \ldots, a+6 d, a+7 d$, their sum is $15 a$, and the difference between the largest and the smallest terms is $14 d$. The largest $d$ such that $14 d \leq 999$ is $d=71$. Thus the largest possible value for $a$ is $999-7 \cdot 71=502$. The maximal sum of the sequence is therefore $15 a=\mathbf{7 5 3 0}$.

Final answer: 7530