River-Crossing Problems

1. River-Crossing Problems Kristy Martin Dan Savage

2. Farmer, Goat, Beans, and Fox • Once upon a time a farmer went to market and purchased a fox, a goose, and a bag of beans. On his way home, the farmer came to the bank of a river and hired a boat. But in crossing the river by boat, the farmer could carry only himself and a single one of his purchases - the fox, the goose, or the bag of the beans. • If left alone, the fox would eat the goose, and the goose would eat the beans. • The farmer's challenge was to carry himself and his purchases to the far bank of the river, leaving each purchase intact. How did he do it?

3. Solution • Bring goose over • Return • Bring fox or beans over • Bring goose back • Bring beans or fox over • Return • Bring goose over

4. Missionaries and Cannibals • In the missionaries and cannibals problem, three missionaries and three cannibals must cross a river using a boat which can carry at most two people • If there are missionaries present on the bank, they cannot be outnumbered by cannibals (because the cannibals would eat the missionaries) • The boat cannot cross the river by itself with no people on board

5. Jealous Husband Problem • In changing women to cannibals and men to missionaries, any solution to the jealous husbands problem will also become a solution to the missionaries and cannibals problem. • In the jealous husbands problem, no woman can be in the presence of another man unless her husband is also present. Also, there cannot be both women and men present on a bank with women outnumbering men.

6. Solution

7. River IQ Test • This game originated as an IQ job applicant test in China • The object is to get everyone (father, two sons, mother, two daughters, police officer and thief) from one side of the river to the other whilst adhering to certain rules. • RULES: At most two persons on the raft at any time • The father cannot stay with any of the daughters without their mother's presence • The mother cannot stay with any of the sons without their father's presence • The thief (striped shirt) cannot stay with any family member if the police officer is not there • Only the father, the mother and the police officer know how to operate the raft

8. Solution • There are only two possible sequences of moves that will accomplish the goal in the least number of steps. (The two solutions are essentially the same; the genders of the parents and children are switched from one to the other.)