A farmer must cross a river with a wolf, a goat and a cabbage. Your boat can only carry the farmer and one of the three elements. If you leave the wolf alone with the goat, the wolf will eat it. If you leave the goat alone with the cabbage, the goat will eat it. How can he cross the river with everything intact?
Riddle documented in the Tang dynasty, 9th century
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The crossing of the river (classical China)
Hints
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- Key restriction: Never leave wolf+goat or goat+cabbage alone together on the same shore.
- Start by crossing with the goat. If you take the wolf or the cabbage first, you leave a forbidden pair.
- From there, the safe sequence is: return alone, cross with wolf, return with the goat, cross with the cabbage, return alone and cross with the goat.
Solution
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Answer: Sequence of crossings:
- The farmer crosses with the goat $\to$ (leaves goat on the other side)
- The farmer returns alone
- The farmer crosses with the wolf $\to$ (leaves wolf)
- The farmer returns with the goat $\to$ (brings back the goat)
- The farmer crosses with col $\to$ (leaves cabbage with wolf)
- The farmer returns alone
- The farmer crosses with the goat $\to$ (end)
Key: The goat crosses the river three times (one way, one way, one way). It is the only element that is never left alone with another dangerous element.
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