River crossing puzzles are a classic form of logic puzzle. In them, you’re provided with a scenario—some number of entities trying to cross a river using a raft or boat—and a set of constraints (typically, some of the entities might eat each other under certain circumstances).
In the TED-Ed video below, we tackle a variant of the puzzle in which a group totaling six, three lions and three wildebeest, need to cross a river using a raft.
Only two animals can go at once. The problem is, if the lions ever outnumber the wildebeest, they’ll eat them. How can they all cross the river?
The larger question of this puzzle is how should we solve such puzzles? In the video, the narrator walks through this solution, but explains how it can be generalized by drawing up decision trees.
At each step of the puzzle, you lay out all the possible options, then cross out any that don’t work.
As you proceed, the set of possibilities dwindle until you’re left with only a few viable paths.
Here are the conditions for this puzzle (also listed in the video):
1. The raft needs at least one animal to paddle it across the river, and it can hold at most two animals.
2. If the lions ever outnumber the wildebeest on either side of the river (including the animals in the boat if it’s on that side), they’ll eat the wildebeest.
3. The animals can’t just swim across, and there are no tricks; the animals have to use the boat as described.
Tune in to see how it’s done: