The `Missionaries and Cannibals' problem is well known as an example of a problem which can be solved by exhaustive search. The problem is that three missionaries and three cannibals want to cross a river by a boat that can only carry one passenger (in addition to the single person needed to row the boat). If the cannibals ever outnumber the missionaries (on either bank) then the missionaries will be eaten. How can they all cross over without anyone being eaten?