A farmer must get a wolf, a goat and a bundle of cabbage across a river. His boat carries himself and at most one of the three. Left alone together, the wolf eats the goat, and the goat eats the cabbage. Counting every single trip in either direction as one crossing, what is the least number of crossings needed to get all three across safely?

The goat is the one that cannot be left with either of the others, so it must travel first and it must come back at one point. Take the goat over; return empty; take the wolf over; bring the goat back; take the cabbage over; return empty; take the goat over. That is 7 crossings, and at no moment are the wolf and goat, or the goat and cabbage, left alone together. The traps: 5 is the tempting plan of goat, back, wolf, back, cabbage — but that leaves the wolf alone with the goat on the far bank; 6 is the good plan with the second empty return forgotten, which leaves the goat stranded; 9 adds one needless there-and-back.