Missionaries and Cannibals Puzzle Answer: 11 Trips [Solved]

The missionaries cannibals puzzle answer is 11 trips. Three missionaries and three cannibals can all cross the river safely in 11 boat trips, and no shorter plan works. The full crossing table is below, with both banks checked after every trip.

Here is the question, as it appears in interview question collections on Glassdoor and GeeksforGeeks. Three missionaries and three cannibals stand on one bank of a river. A boat carries at most two people, and it cannot cross empty, so someone must row it each way. If cannibals ever outnumber missionaries on either bank while at least one missionary is there, the missionaries get eaten. Can all six reach the far bank, and if so, how?

The puzzle is old: it goes back to a river-crossing problem in Alcuin of York’s collection from around AD 800, and it became a textbook example of state-space search in 1968. Interviewers still use it, because the gap between finding an answer and understanding it is what they want to measure.

The Question, Stated Plainly

Three missionaries and three cannibals. One boat, two seats, no empty crossings. One rule: on either bank, missionaries must never be outnumbered by cannibals while a missionary is present. In other words, a bank with no missionaries is safe, whatever the cannibal count. The boat counts too, because its passengers are checked with the bank it leaves and the bank it reaches.

Two facts shape the whole solution. First, someone must always row the boat back, so every forward trip except the last one costs a return trip. Second, the opening move is nearly forced: two cannibals across is the clean start, because sending two missionaries first strands the one left behind with three cannibals.

The Missionaries Cannibals Puzzle Answer in 11 Trips

Here is the full plan. M means missionary, C means cannibal. After each trip, both banks are safe.

Trip	Boat carries	Left bank after	Right bank after
1	2 cannibals cross	3M, 1C	0M, 2C
2	1 cannibal returns	3M, 2C	0M, 1C
3	2 cannibals cross	3M, 0C	0M, 3C
4	1 cannibal returns	3M, 1C	0M, 2C
5	2 missionaries cross	1M, 1C	2M, 2C
6	1 missionary and 1 cannibal return	2M, 2C	1M, 1C
7	2 missionaries cross	0M, 2C	3M, 1C
8	1 cannibal returns	0M, 3C	3M, 0C
9	2 cannibals cross	0M, 1C	3M, 2C
10	1 cannibal returns	0M, 2C	3M, 1C
11	2 cannibals cross	0M, 0C	3M, 3C

Read the table from top to bottom and check each row against the rule. After trip 1, the left bank holds 3 missionaries and 1 cannibal, which is safe, and the right bank holds only cannibals. By trip 5, both banks hold equal numbers, 1 and 1 on the left and 2 and 2 on the right. Once trip 7 is done, all three missionaries are across, and the remaining cannibals can ferry themselves over. Finally, trip 11 empties the left bank, and the puzzle is done.

Notice the pattern. The first four trips move the cannibals across in stages, the middle three move the missionaries, and the last four bring the remaining cannibals over. Trip 6 is the hinge: one missionary and one cannibal row back together so the last missionary can cross on trip 7.

Why the Missionaries Cannibals Puzzle Answer Is 11 Trips

In fact, eleven is not just a plan that works. It is the shortest plan that works, and the reason is simple arithmetic plus the safety rule.

Start with the arithmetic. The boat holds two people, and six people must end up on the far bank. If every forward trip carried two people and every return carried one, the crossing would take 5 forward trips and 4 returns: 9 trips in total. So 9 is the floor set by counting alone. Ten trips is impossible, because the boat must finish on the far bank, so forward trips always outnumber return trips by exactly one, and the total is always odd. That leaves 9 or 11.

Now the safety rule blocks the 9-trip shape. That shape needs missionaries moving early and in pairs, but sending two missionaries first strands the one left behind, and the safe openings spend extra return trips first. The full state space of legal positions has been mapped, and 11 is the shortest path through it. So the missionaries cannibals puzzle answer is 11 trips because 9 is blocked by the rule and 10 is blocked by the boat having to end on the far side.

The Trap Most Candidates Fall Into

The missionaries cannibals puzzle answer hides three traps, and the first one catches most people in the opening seconds. Most candidates send two missionaries across first, because moving the people who need protection feels like the priority. It is the worst possible first move: one missionary stays behind with three cannibals, and the puzzle ends on trip 1. The safe instinct is the opposite one: move the cannibals first, while the missionaries wait in a group too big to threaten.

The second trap is trip 6. By trip 5, two missionaries are across and the plan feels like it is working. Then the correct move is to row one missionary and one cannibal back to the start, which feels like undoing the progress. Candidates who refuse to go backwards get stuck here, sending pairs forward and stranding the last missionary every time. The puzzle rewards the candidate who treats a return trip as part of the plan, not as a failure.

The third trap is checking only one bank. Every crossing changes both banks at once, and the rule applies to both, so a move that looks safe on the bank the boat leaves can be fatal on the bank it reaches. The fastest solvers write down both banks after every trip instead of holding the numbers in their head.

What the Interviewer Is Actually Testing

This puzzle is not a test of river knowledge. It is a test of how you handle a problem with a hard constraint and a small state space.

First, the interviewer watches whether you check the constraint after every move, not just at the end. A plan that works for ten trips and breaks the rule on the eleventh is a failed plan, and the interviewer wants to see you catch that yourself.

Second, they watch how you handle the counterintuitive move. Trip 6 sends people backwards, and strong candidates accept it as soon as they see it opens the crossing. Weak candidates argue with the puzzle instead.

Third, they watch whether you work systematically. The puzzle has only a handful of legal positions, so a candidate who lists the options at each step will find the answer, while a candidate who guesses will loop. That is why interviewers like this question: it separates careful search from lucky guessing in under five minutes.

Finally, the follow-up question matters as much as the answer. A good interviewer asks whether four missionaries and four cannibals could cross in the same boat. The answer is no: with four pairs, the boat is too small, and no legal sequence exists. If you can explain why the 3-and-3 case works and the 4-and-4 case cannot, you understand the puzzle instead of memorising it.

Try Another River Puzzle

If you liked this crossing, the wolf, goat and cabbage puzzle is the same idea in a smaller boat: a farmer must ferry a wolf, a goat and a cabbage across a river, one at a time, without leaving the goat alone with the cabbage or the wolf alone with the goat. We have solved it step by step here: Wolf Goat Cabbage Puzzle Answer [Solved].

For a probability puzzle in the same series, try the broken stick puzzle, where two random cuts leave a triangle only a quarter of the time: Broken Stick Puzzle Answer: 1 in 4 [Solved].

Frequently Asked Questions

Can the boat carry only one person?

Yes, but it wastes trips. A one-person crossing still needs someone to row back, so it adds two trips and moves nobody forward. No shortest plan uses a solo crossing.

What if the boat held three people?

Then the crossing takes 5 trips: three cannibals cross, one returns, three missionaries cross, one cannibal returns, and the last two cannibals cross. As a result, the bigger boat removes the bottleneck that forces 11 trips.

Is the missionaries cannibals puzzle answer really 11 trips?

Yes. Eleven trips is the shortest legal plan, and the table above is one complete 11-trip solution. Shorter plans fail either on the counting, because the boat must end on the far bank, or on the safety rule, because an early missionary move strands someone.

Sources: the question appears in Glassdoor interview question collections and in the GeeksforGeeks Interview Prep page on missionaries and cannibals; the history and the shortest-path result are covered in the Wikipedia article on the missionaries and cannibals problem.