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Three missionaries and three cannibals start on the left bank of a river. They have a rowboat with them that holds at most two people that can be used to transport people across the river (assume the rowboat can be rowed by either a missionary or a cannibal). Assuming that at no time the number of cannibals can outnumber the missionaries on either bank of the river how can all three missionaries and all three cannibals be transported safely across the river to the right bank.

My answer would be to take a cannibal over first, then take a missionary, then another, and then you have 2 missionaries and 1 cannibal on the right, and 1 missionary and 1 cannibal still on the left with a cannibal crossing back but then that wouldn't work because now you will have a cannibal crossing back over to the left to pick up another person which will lead to 2 cannibals and 1 missionary.

Adam
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  • http://en.wikipedia.org/wiki/Missionaries_and_cannibals_problem – Robert Israel Mar 04 '14 at 05:02
  • Alright so I can solve it now, but I'm in Discrete Math right now and the topic that we are in is one to one and onto functions, as well as vertices and edges. I'm pretty sure one of these topics relates to this problem and I'm wondering which topic does. How could you solve this problem using Discrete Math? – Adam Mar 04 '14 at 16:24
  • Construct the graph whose vertices are the allowed states (numbers of cannibals and missionaries on each bank and position of the boat) and edges joining two states if one move takes you from one to the other. Find a path in this graph from the initial state to the desired final state. – Robert Israel Mar 05 '14 at 02:30

1 Answers1

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YouTube Video explains it.

Google Search for "3 missionaries 3 cannibals".

Wikipedia article on it and the closely related 'jealous husbands' problem.

What's the point in me reiterating the same solution?

Guy
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