Three missionaries and three cannibals must cross a river using a boat that can hold only two people at a time. The missionaries are afraid of being outnumbered by cannibals at any location. Furthermore, only one missionary and one cannibal know how to row the boat. How can they all safely get across the river?

Answer

Yes, all six can cross the river safely, even with the rowing restriction and the fear of missionaries being outnumbered.

Solution

Let’s label the missionaries as M, m, m and the cannibals as K, k, k, where M (missionary) and K (cannibal) are the only ones who can row the boat.

  1. K (the rowing cannibal) takes k across the river.
  2. K returns alone.
    (Now: K, M, m, m on the original side; k, k on the far side)
  3. M and m cross together.
  4. M and k return.
    (Now: K, K, M, m on far side; M, k, m on original side)
  5. The other M and m cross again.
  6. K returns alone.
    (Now: K, k, k on original side; M, m, m on far side)
  7. Finally, K takes k across, returns, and then ferries the last k across.

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