Missionaries and Cannibals Puzzle — Solution

As I’ve mentioned in the problem statement, this problem is quite hard for humans and might be very easy for a machine to solve (with the right formalization of course). The reason is that this problem can contain infinitely many repeated states. If we don’t keep track of states we have been in, we could easily end up going in rounds with the same man in the boat for infinity. Thus, we have to keep track of states we have been in, and do not repeat them, since getting back to them, means that all the “progress” we made has put us back, and therefore was useless.

Another thing to pay attention is that it really doesn’t matter which one of the missionaries will we get into the boat first/second or third. This is also true regarding the cannibals. In fact this small note saves us a lot of states space, making this problem very simple indeed, when treated properly.

Therefore, if you still want to try solve it, try drawing all possible situations while not distinguishing any importance given to the order between different missionaries and cannibals, and keeping track of repeated states as well.

Solution:

MMMCCC  |   |

Missioner and a Cannibal go, Missioner comes back

MMMCC  |   |  MC      MMMCC  |   |  C

Two Cannibals go, one comes back

MMM  |   |  CCC    MMMC |   |  CC

Two missioners go, Missioner and a Cannibal come back

MC  |   |  CCMM     MMCC  |   |  CM

Two missioners go, the cannibal brings the boat back

CC  |   |  CMMM    CCC  |   |  MMM

Now all the cannibals can get to the other shore easily one by one: two go, one comes back.

One thought on “Missionaries and Cannibals Puzzle — Solution

  1. Pingback: Life by Bits & Numbers » Missionaries and Cannibals Puzzle

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