Talk:2010 AMC 10B Problems/Problem 24

Apologies if this amounts to trolling, but I ran across this problem helping my child. Using brute force, I constructed a solution that makes this problem's answer not only nonunique, but my counterexample leads to one of the incorrect answers. Examining the official solution, there is no requirement for coefficient 'a' to be equal for both progressions. The only required relation between the two sequences is that they total one point apart. I began with geometric progressions starting at 1 with powers of 1-4 and found that only 2 and 4 produce odd totals, but only 4 allows for an arithmetic progression.

Here's my counterexample:

Raiders box score: 1 4 16 64 = 85 Wildcats box score: 9 17 25 33 = 84

First half score is 31 (answer B). Did I miss something?

The problem starts:

A high school basketball game between the Raiders and Wildcats was tied at the end of the first quarter.

This is why $a$ must be the same for both progressions.