Lions and Bulls

On one bank of a river, there are three lions and three bulls.

There is one boat available that can hold up to two animals, and they would like to use it to cross the river.

If the lions ever outnumber the bulls on either of the river's banks, the bulls will get eaten.

How can the boat be used to safely carry all three bulls and three lions across the river?

Left Bank

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Right Bank

Solver

Load the optimal plan when you like.

Tap animals to load/unload the boat (max 2). You won’t lose on mistakes — we’ll warn you if a bank becomes unsafe.

Answer

Solution

We represent each step in the format:
(Left Bank: Lions, Bulls | Right Bank: Lions, Bulls | Boat Location)

Initial state:
(3L, 3B | 0L, 0B | Left)

Step 1: Lion and Bull cross →
(2L, 2B | 1L, 1B | Right)

Step 2: Lion returns ←
(3L, 2B | 0L, 1B | Left)

Step 3: Two Bulls cross →
(3L, 0B | 0L, 3B | Right)

Step 4: One Bull returns ←
(3L, 1B | 0L, 2B | Left)

Step 5: Two Lions cross →
(1L, 1B | 2L, 2B | Right)

Step 6: One Lion returns ←
(2L, 1B | 1L, 2B | Left)

Step 7: Two Bulls cross →
(2L, 0B | 1L, 4B | Right)

Step 8: One Bull returns ←
(2L, 1B | 1L, 3B | Left)

Step 9: Two Lions cross →
(0L, 1B | 3L, 3B | Right)

Step 10: One Lion returns ←
(1L, 1B | 2L, 3B | Left)

Step 11: One Lion and one Bull cross →
(0L, 0B | 3L, 3B | Right)

🎉 Final State:
All animals are safely across the river!
(0L, 0B | 3L, 3B | Right)

At every point during the journey, the number of bulls was never less than the number of lions on either side.

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