River-Crossing Problems

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River-Crossing Problems - PowerPoint PPT Presentation

River-Crossing Problems. Kristy Martin Dan Savage. Farmer, Goat, Beans, and Fox.

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River-Crossing Problems

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Presentation Transcript

River-Crossing Problems

Kristy Martin

Dan Savage

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?
Solution
• Bring goose over
• Return
• Bring fox or beans over
• Bring goose back
• Bring beans or fox over
• Return
• Bring goose over
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
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.
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
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.)