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Missionaries and cannibals

It is a classic of delicate maneuvers: moving forward does not always mean getting closer to the solution. The good thing about the problem is learning to recognize which positions are safe and which only seem to be so.

Three missionaries and three cannibals must cross a river in a boat that only accepts one or two people. On no shore can there remain a group in which the cannibals outnumber the missionaries, unless there are no missionaries on that shore.

How can everyone cross safely?

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Hints

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Don't just seek to progress; Sometimes you have to go back to avoid leaving a shore in a prohibited situation.
Return trips matter as much as outbound trips.
It is best to open a secure transit configuration first.

Solution

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Answer: Yes. Everyone can cross in 11 routes. A valid sequence (M = missionary, C = cannibal) is:

CC ->
C <-
CC ->
C <-
MM ->
MC <-
MM ->
C <-
CC ->
C <-
CC -> Explanation: The idea is to first use the cannibals to transport the boat without ever leaving the missionaries in a minority on a shore where there are cannibals. When the three missionaries can cross safely, the transfer is completed. It is not about moving “reasonable couples”, but about always preserving the critical condition on both shores.

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