The Fox, Chicken and Grain River-Crossing Riddle
A farmer must cross a river with a fox, a chicken, and a sack of grain in a boat that holds only the farmer plus one. The fox eats the chicken and the chicken eats the grain when the farmer is absent. What is the minimum number of one-way trips to get everyone across?
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What is the answer to the fox, chicken and grain river-crossing riddle?
The minimum is 7 one-way trips. The farmer first takes the chicken across, returns alone, then takes the fox (or grain), brings the chicken back, takes the grain (or fox), returns alone, and finally takes the chicken across again.
Why does the chicken have to come back across?
The chicken is the linking item: it can't be left with the fox (the fox eats it) or with the grain (it eats the grain). So the farmer ferries it back mid-puzzle to keep the dangerous pairs apart, which is why 7 trips are needed.
Can you solve the fox, chicken and grain puzzle in fewer than 7 trips?
No. Because something is always left alone on a bank, you must shuttle the chicken back at least once, making 7 one-way trips the proven minimum.