I recently bought the book The Art and Craft of Problem Solving, by Paul Zeitz. I highly recommend this book if you want to build problem-solving skills. The book explores some problem-solving strategies and tactics, and then presents related problems.
The best way of learning to do something is trying, and the book provides plenty of problems to try: it has about six hundred problems, mostly without solutions. Many of the problems are quite difficult, most are very enjoyable.
This is one of the first (and easiest) problems in the book:
Indiana Jones needs to cross a flimsy rope bridge over a mile-long gorge. It is so dark that it is impossible to cross the bridge without a flashlight. Furthermore, the bridge is so weak that it can only support the weight of two people. The party has just one flashlight, which has a weak beam, so whenever two people cross, they are constrained to walk together, at the speed of the slower person. Indiana Jones can cross in five minutes. His girlfriend can cross in 10 minutes. His father needs 20 minutes, and his father’s sidekick needs 25 minutes. They need to get everyone across safely in one hour to escape the bad guys. Can they do it?
Can you solve it?