The fox, goose and bag of beans puzzle is a mental puzzle originating from an old riddle.
The story
Once upon a time a farmer went to market and purchased a fox, a goose, and a bag of beans. On his way home, the farmer came to the bank of a river and hired a boat. But in crossing the river by boat, the farmer could carry only himself and a single one of his purchases - the fox, the goose, or the bag of the beans.
If left alone, the fox would eat the goose, and the goose would eat the beans.
The farmer’s challenge was to carry himself and his purchases to the far bank of the river, leaving each purchase intact. How did he do it?
Solution
The first step must be to bring the goose across the river, as any other will result in the goose or the beans being eaten. When the farmer returns to the original side, he has the choice of bringing either the fox or the beans across. If he brings the fox across, he must then return to bring the beans over, resulting in the fox eating the goose. If he brings the beans across, he will need to return to get the fox, resulting in the beans being eaten. Here he has a dilemma, solved by bringing the fox (or the beans) over and bringing the goose back. Now he can bring the beans (or the fox) over, leaving the goose, and finally return to fetch the goose.
His actions in the solution are summarised in the following steps:
- Bring goose over
- Return
- Bring fox or beans over
- Bring goose back
- Bring beans or fox over
- Return
- Bring goose over
Thus there are seven crossings, four forward and three back.
Variations
Many variations exist of the three objects (eg. wolf, goat and cabbage or fox, duck and sack of corn), but the central logic remains the same, being A eats B and B eats C. They are all part of the generic category of river crossing puzzles where the object is to move a set of pieces across a river subject to various restrictions. The answer in one lateral thinking variant has the goose swim across the river. A version of this puzzle was published by Lewis Carroll, and is sometimes attributed to him, but it is much older, as is attested by an illustration of it in the illumination of a medieval manuscript.
See also
- Missionaries and cannibals problem
- Transport puzzle
External links
- Goat, Cabbage and Wolf A Java simulation
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