Here's a Jeopardy Thought Puzzle.

For whatever reason, I can't stop thinking about this:

I'm watching the Jeopardy college tournament the other day, and Alex is talking to the contestants about the wildcard spots for high scores, saying something like, "One, two, maybe all three of you can move on to the finals".

It got me thinking. Does Trebek really know that for sure?

Which then got me thinking:

"If every possible star aligned and each contestant were able, with 100% accuracy, predict the daily doubles, then what is the maximum score of a three-way tie, if they were working together to game the outcome to achieve a maximum 3way tie?

Or think Watson playing itself in jeopardy a billion times trying to achieve a three-way tie with itself. You know things are bad when you start having three-ways with yourself.

Anyways, such a dumb thing to think about, but had to share to be done with it. I'm pretty sure I figured it out but now even doubting myself. It is a little tricky with daily doubles.

Trying to think how to write it out algebraically, but don't know how that works having different rounds.

Hint:

Double Jeopardy-
6 categories
5 questions this time worth double
$400-$800-$1200-$1600-$2000
2 daily doubles

Final Jeopardy-
one question to risk it all.

What is the maximum score for a three-way tie?