Took me a second to realize why 289. 17 * 17. One dollar per square. If you could get him to offer a prize for a 1000 * 1000 grid, you have quite a nice reward.
You're not being serious, I know, but I'll answer seriously anyway. 1000x1000 is not an edge case - it can't be done - so offering a reward for a solution is pretty pointless.
A related and unsolved question (and thus legitimate) could be: what is the smallest c such that 1000x1000 is c-colorable.
The problem with that is knowing that you have the minimum. The good thing about the question as asked is that it's asking for something specific and not a proof of impossibility. Your question is legitimate and interesting, but requires a proof of minimality.
That's difficult.
A different question would be "who can come up with the smallest c in 6 months", which probably wouldn't yield the true answer, but for a $1M prize it might come quite close (and could lead to some interesting theoretical advancements).
> That's difficult
Agreed, but that is why it would be worth $1M :-).