Missionaries and Cannibals Solution: 11 Crossings, Step by Step
In the classic puzzle, three missionaries and three cannibals must cross a river in a boat that holds two. The cannibals must never outnumber the missionaries on a bank where there is at least one missionary. The shortest solution takes 11 crossings: send two cannibals over, bring one back, send two cannibals over again, bring one back, then send two missionaries, bring one of each back, and so on. The full list, with a picture of every crossing, is below.
The puzzle and its one rule
Three missionaries and three cannibals stand on one bank of a river. There is one boat, and it holds at most two people. Someone must row, so the boat can never cross empty. The goal is to get all six to the far bank.
The rule: if the cannibals outnumber the missionaries on a bank, the missionaries there are eaten. A bank with no missionaries is always fine, and so is the boat itself while it sails. That single rule is what makes the puzzle hard, because the dangerous moments happen on the *banks* after the boat has left.
The pictures below use the same puzzle in its friendlier form, the one you play in River Crossing: chickens are the missionaries and foxes are the cannibals. Foxes may never outnumber the chickens on a bank that has chickens on it.
The solution, crossing by crossing
Each row shows who is on each bank while the boat sails, who is in the boat, and which way it goes. There are 11 crossings. The first six are here:
And the last five. After crossing 11 everyone is on the far bank:
The same solution as a list (M = missionary, C = cannibal):
- Two C cross to the far bank.
- One C rows back.
- Two C cross again. All three cannibals are now on the far bank.
- One C rows back.
- Two M cross. The far bank now has two missionaries and two cannibals; the start bank has one of each.
- One M and one C row back together.
- Two M cross. All three missionaries are now on the far bank, and the start bank holds two cannibals.
- One C rows back.
- Two C cross.
- One C rows back.
- The last two C cross. Everyone is across.
11 is the fewest possible crossings. There are four different 11-crossing solutions (two of them start by sending one missionary and one cannibal over together), but none is shorter, and your River Crossing stars count your crossings against this par.
How to think about it
Almost every wrong turn in this puzzle comes from checking only the boat. Check both banks after every crossing, the one the boat just left and the one it just reached.
- Moving the cannibals first is safe, because a bank that has no missionaries on it can hold any number of cannibals. That is why the solution begins with three cannibal crossings.
- The swap in the middle is the heart of the puzzle. Crossing 6 brings one missionary and one cannibal back together, so that neither bank ever has the cannibals ahead.
- Rowing someone back is not a mistake. Every solution has crossings that go backwards. A crossing back is there to keep both banks safe, not to make progress.
- When you are stuck, undo. Count the animals on each bank. If it is the foxes that are ahead on a bank with chickens, step back one crossing and try the other pairing.
Other versions of the puzzle
The fox, the chicken and the grain
An older puzzle with the same shape: a farmer must take a fox, a chicken and a sack of grain across a river in a boat that holds the farmer and one passenger. Left alone, the fox eats the chicken and the chicken eats the grain. It takes 7 crossings: chicken over, back alone, grain over, chicken back, fox over, back alone, chicken over.
Bigger groups need bigger boats
With two pairs and a two-seat boat the puzzle takes just 5 crossings. With three pairs it takes 11. With four or more pairs and a two-seat boat there is no solution at all: that is why the harder levels give you a bigger boat. Four pairs need a boat for three (9 crossings), five pairs a boat for three (11), six pairs a boat for four (9).
Fewest crossings for the classic rule (cannibals may not outnumber missionaries on a bank with missionaries).
| Pairs | Boat holds | Fewest crossings |
|---|---|---|
| 2 | 2 | 5 |
| 3 | 2 | 11 |
| 4 | 2 | No solution |
| 4 | 3 | 9 |
| 5 | 3 | 11 |
| 6 | 4 | 9 |
Try it yourself
River Crossing has seven levels, from the farmer and the fox to six pairs, a Daily river that is the same for everyone, and a Teach me button that tells you the next crossing when you are stuck. Three stars means matching the fewest crossings above.
Frequently asked questions
What is the solution to the Missionaries and Cannibals puzzle?
Eleven crossings: two cannibals over, one back, two cannibals over, one back, two missionaries over, one missionary and one cannibal back, two missionaries over, one cannibal back, two cannibals over, one back, two cannibals over. Every crossing is shown with pictures above.
What is the minimum number of crossings?
Eleven for three missionaries, three cannibals and a boat that holds two. No solution is shorter.
Why can't the cannibals outnumber the missionaries?
That is the rule of the puzzle: on any bank that has at least one missionary, the cannibals may not be more than the missionaries, or the missionaries are eaten. A bank with no missionaries is always safe.
Can the boat cross with nobody in it?
Not in the classic puzzle. Someone has to row, so every crossing carries one or two people. In the farmer version the farmer rows and can cross alone.
Is there a solution with four missionaries and four cannibals?
Not with a two-seat boat. With four pairs the boat has to hold three, and then the shortest solution is 9 crossings.
How many crossings does the fox, chicken and grain puzzle take?
Seven: take the chicken over, return alone, take the grain over, bring the chicken back, take the fox over, return alone and take the chicken over again.
Can I play it online for free?
Yes. River Crossing on GameLake is free in your browser, with seven levels, a Daily river and a Teach me button. No download and no account.