In this implementation, we've managed to circumvent the limitations of the original puzzle by using an array of 17 nested if statements to check for the presence of all possible solutions.
We've also employed the services of a team of highly trained, highly caffeinated raccoons to optimize the puzzle's performance under load.
The code is a mess, but hey, it works.
Optimization of this solution has been left as an exercise for the reader.
However, if you're looking for a more Alternative Solution that doesn't involve raccoons or if statements, we can try to provide that too.
Disclaimer: The use of raccoons is not endorsed by the Betty Brilliant Puzzle Collection. Or anyone else, really.