How can various combinations of people, animals, and things get across a river when there are restrictions on how many can be in the boat, or together on the bank?
A fox, a duck, and a bag of corn (or a wolf, a goat, and cabbage) If left alone, the fox will eat the duck and the duck will eat the corn. Only one can fit in the boat in addition to the rower.
Three missionaries and three cannibals The cannibals will eat the missionaries if they outnumber them in the boat or on the bank. Only two people can fit in the boat.
Missionaries and cannibals again, but only one of each can row (also three humans, one big monkey and two small monkeys)
Three jealous husbands and their wives None of the wives can be left in the presence of another man without their husband present. The boat holds two. Two men and one woman row.