It's probably a lot cheaper to crowd source the solution. You'll get a lot more effort for the money. Crowd sourcing a problem for a prize is a well proven method that's centuries old. Here are some famous examples:
The one improvement would be to crowd-source the challenges and the money. Think KickStarter but participants vote for the projects and donate the prize money.
melling|11 years ago
http://en.wikipedia.org/wiki/Longitude_prize
http://en.wikipedia.org/wiki/Spirit_of_St._Louis
And of course, the modern X-Prizes: http://x-prize.com
The one improvement would be to crowd-source the challenges and the money. Think KickStarter but participants vote for the projects and donate the prize money.