Me:
I have a wolf, a goat, and a cabbage and a boat. I want to get them all across the river. If I leave the goat and the wolf together, the goat will eat the wolf. If I leave the wolf and the cabbage together, the wolf will eat the cabbage. I can only take one at a time. How do I do it?
o1-pro:
This puzzle is simply a twist on the classic “Wolf, Goat, and Cabbage” riddle, except here the dangerous pairs are:
Goat & Wolf cannot be left alone (the Goat will eat the Wolf).
Wolf & Cabbage cannot be left alone (the Wolf will eat the Cabbage).
The only “safe” pair to leave alone is Goat & Cabbage. You can ferry them across one at a time without ever leaving the dangerous pairs together by following these steps:
Take the Wolf across
Near bank: Goat, Cabbage
Far bank: Wolf
Return empty
Near bank: Goat, Cabbage, Boatman
Far bank: Wolf
Take the Goat across
Near bank: Cabbage
Far bank: Wolf, Goat, Boatman
Since Goat & Wolf can’t be left alone, you must immediately bring one back in the next step.
Bring the Wolf back
Near bank: Wolf, Cabbage, Boatman
Far bank: Goat
Take the Cabbage across
Near bank: Wolf
Far bank: Goat, Cabbage, Boatman
Goat & Cabbage are safe together.
Return empty
Near bank: Wolf, Boatman
Far bank: Goat, Cabbage
Finally, take the Wolf across
Near bank: (empty)
Far bank: Wolf, Goat, Cabbage, Boatman
Me:
I have a wolf, a goat, and a cabbage and a boat. I want to get them all across the river. If I leave the goat and the cabbage together, the cabbage will eat the goat. If I leave the wolf and the cabbage together, the wolf will eat the cabbage. I can only take one at a time. How do I do it?
o1-pro:
This version of the riddle is basically the “wolf, goat, and cabbage” puzzle with the roles reversed for who can safely be left behind. The key is that the only pair you can leave alone is the goat and the wolf. You cannot leave the goat and cabbage together (the cabbage eats the goat!), nor the wolf and cabbage together (the wolf eats the cabbage!).
A workable step‐by‐step solution is:
Take the cabbage across first.
Left bank: Wolf, Goat
Right bank: Cabbage
Return alone to the left bank.
Left bank: Wolf, Goat, (You)
Right bank: Cabbage
Take the goat across.
Left bank: Wolf
Right bank: Goat, Cabbage, (You)
(You cannot leave goat and cabbage together, so…)
Bring the cabbage back with you to the left bank.
Left bank: Wolf, Cabbage, (You)
Right bank: Goat
Take the wolf across.
Left bank: Cabbage
Right bank: Goat, Wolf, (You)
Return alone to the left bank.
Left bank: Cabbage, (You)
Right bank: Goat, Wolf
Finally, take the cabbage across once more.
Left bank: (empty)
Right bank: Wolf, Goat, Cabbage, (You)
All three—the wolf, the goat, and the cabbage—are now safely across without ever leaving a “forbidden” pair alone.