On this Memorial Day weekend, a military-themed example of how an analytic solution could improve a computed solution:
"The US army in Korea is equipped with Paladin anti-artillery guns that can trace enemy shells back to the guns and fire shells at the enemy guns with pin-point accuracy. However, it takes for the Paladins about 10 min to locate the enemy guns, during which time the Paladins would be targeted by the enemy guns Gen. Thomas A Schwartz, a former US army commander in Korea, stated that the US army in Korea would be destroyed in less than three hours."
His answer is 15 pages long and he left out explanations of steps so he wouldn't go over the limit set by Jugend forscht (youth researches). I'd assume they'll give it a work over before releasing it.
http://news.ycombinator.com/item?id=4029676 <- Lots of comments, no substance, now dead.
http://news.ycombinator.com/item?id=4028756 <- Observing there are no details anywhere
http://news.ycombinator.com/item?id=4029599 <- Ditto.