You're right on both accounts: your solution and @spark beating you to it.

I guess there's a bit of a problem with this set-up if one wants to solve without hints while, at the same time, knowing whether they're wasting their time regarding the prize (checking comments for the right answer).

Unfortunately, I'm not sure if there's any way to get around this issue.

In any case, I thank you for giving it a try and I congratulate you on your correct solution.