A logic puzzle.
A farmer is taking his produce to market. He has a fox, a hen, and a bag of grain. (No, I have no idea what he's doing with a fox. You don't normally farm foxes, let alone take them to market, but this is a very old story and folks were different in those days.)
Now, as I'm sure you all know, foxes like to eat hens. And hens (when they can avoid the foxes) love to snack on a bit of grain. But foxes don't like grain (this becomes important later).
As long as the farmer is watching over them, the fox and the hen will be as good as gold. But if he leaves them alone, well it's quite obvious what will happen. The hen will eat the grain or the fox will eat the hen. And that, of course, would be bad news for the farmer's profits.
On the way to the market is a river. When the farmer gets to the river, he sees that the ferry isn't there. The only way across is in a tiny rowing boat. But this boat is so small that he can only take one item at a time. He will have to make several trips. But wait! While he's in the boat with one item, how will he stop the two left on the bank from eating each other?
It's an old story, of course. It was first recorded 1200 years ago but it's probably even older than that. I first heard it as a school boy (no, that was not 1200 years ago!). It's a good puzzle to give to young children, with suitable props to help them work it out. (If you have four children, they could act out the parts. One child could "row" the others across the room one-by-one. Then they could eat each other if the "farmer" gets it wrong. That sounds like fun. Well, maybe. . .)
I'm sure you've heard it before and you know the answer to the farmer's dilemma. Even if you haven't heard it before, I'm sure you can work out the solution. Here is the full solution, with helpful diagrams.
Here is our poor farmer's dilemma:
|
Farmer Fox Hen Grain |
. . . . . . . . . . |
To the Market --> |
So, what is the farmer to do? If he takes the fox first, the hen will eat the grain before he gets back. If he takes the grain first, the fox will eat the hen. Aha, but we know that foxes don't like grain! So if he takes the hen first, the fox will sniff hopefully at the sack and turn his nose up at it.
So this is what the farmer does.
|
Fox Grain |
. . . . . . . . . . |
Farmer Hen |
Now the farmer rows back for the next item. It doesn't matter which he takes next, as there is no danger of anything eating anything else at the moment. So he takes the fox over. So far so good.
|
Grain |
. . . . . . . . . . |
Farmer Fox Hen |
Now he has to go back for the grain. But. . . uh-oh. . . while he's gone, guess what the fox will be doing to the hen? Hmm. (Note: if he had taken the grain second and left the fox till last, he would have had the same problem. The hen would eat the grain while he went back for the fox.)
Here's where the clever part comes in. When he goes back for the grain, the farmer takes the hen back with him!
He does what? Surely not? Isn't that just undoing his hard work? Well, yes. But as we all know, you sometimes have to take a step backwards before you can go forwards.
So he takes the hen back and leaves it on the "wrong" bank.
|
Farmer Hen Grain |
. . . . . . . . . . |
Fox |
And he picks up the grain and takes that over to join the fox.
|
Hen |
. . . . . . . . . . |
Farmer Fox Grain |
Now he can safely leave the grain and the fox together (foxes don't eat grain, remember) while he goes back for the hen.
Finally, he brings the hen over and all his goods are on the correct side of the river. He can continue his journey to market without further trouble.
|
. . . . . . . . . . |
Farmer Fox Hen Grain |
To the Market --> |
And that's it! No tricks, no magic. Plain, old-fashioned logic.
© 2001 by David Meadows. All rights reserved. 26 January 2001