A Wolf, a Goat, and a Cabbage

A man finds himself on a riverbank with a wolf, a goat, and a head of cabbage. He needs to transport all three to the other side of the river in his boat. However, the boat has room for only the man himself and one other item (either the wolf, the goat, or the cabbage). In his absence, the wolf would eat the goat, and the goat would eat the cabbage. Show how the man can get all these “passengers” to the other side.

 

Answer:

Let M, w, g, and c stand for the man (with the boat, which is always on the same bank of the river as the man), wolf, goat, and cabbage head, respectively. The following figure depicts two sequences of trips that solve the problem.