The prize should be awarded for either finding a solution, or proving that no solution exists.
Re:The 17x17 problem solved
by JonnieCache on Monday February 13, 2012 @05:50AM
(#3585084)
Yes. The two eventualities are equivalent for this purpose.
Obviously the non-existence of a solution might itself be unprovable, so you'd still have to set some time limit. Oh Gödel, always there to ruin our plans.
Obviously if no solution exists then that fact is also provable, since this is a finite problem. The problem is not that it might not be provable. The problem is that verifying a non-existence proof could be hard, because such a proof would probably be something like "I ran my solver for three weeks and it said that there are no solutions".
I think it could be addressed with a reasonable fallback, such as a math related charity after 20 years or some such. Or if you could make it possible to start awarding 'best tempt' partial payouts.
There are certainly some complications involved, but it still seems workable to me overall. Perhaps partner with a well-known prize-giving organization.