Answer to Puzzle #56: Crossing a River With a Fox, Chicken & Some Grain

56. A farmer is on his way back from the market, with him he has a fox, a chicken and some grain. When he reaches a river crossing he must use a small boat only big enough for him and one other item. Unfortunately if the fox is left alone with the chicken it will eat it, as will the chicken eat the grain. Explain how the farmer can cross the river.

It seems incredible that we have gotten all the way to puzzle number 56 before including this all time favourite. It's fairly easy and many of you will have heard it before, that still doesn't mean there is nothing to learn:

picture of a farmer and a fox in a boat.Before reading the answer can I interest you in a clue?

One of the reasons why this puzzle is easier than we're used to is that at every stage, basically every move available to you, other than reversing your previous move, if it's valid, is the correct move. Lets take a look at the solution and then I'll explain what I mean-
  • The farmer takes the chicken to the far side and leaves him there.
  • The farmer returns in an empty boat and collects the fox (or grain.)
  • Travelling again to the far side he deposits the fox (or grain) & picks up the chicken to return to the near side.
  • At the near side he deposits the chicken and collects the grain (or fox).
  • At the far side he leaves the fox and grain together.
  • He returns with an empty boat and collects the chicken.
Seven crossing all done.

So if we look at the first move, we can't take the fox, the chicken will eat the grain. We can't take the grain, the fox will eat the chicken. All we can do is take the chicken. The only ambiguity is for example on the second move where I say 'collects the fox (or grain.)' I'm trying to indicate that either of these is valid so long as when I refer to 'grain (or fox)' you do the opposite. Again at each of these points if the move is legal it's the answer.

Exposition

This puzzle exists in a lot of forms, I have chosen fox, chicken and grain. Other people talk about fox, goose and beans. Wolf, goat and cabbage. Panther, pig and porridge. Or even some more exotics involving dragons and slaves. The premise is always the same, A can't be left with B, and B can't be left with C. A & C however, are fine. A more pure answer looks like:
  1. Take B
  2. Return
  3. Take A (or C)
  4. Return B
  5. Take C (or A)
  6. Return
  7. Take B
Why am I including this just after the much more difficult problems? Well for one these traditional puzzles are much more popular. There's still stuff to talk about. And it's sort of a classic, no collection of puzzles is complete without it. Plus it's likely that you've seen this before, try to imagine what it looks like if you haven't

One more thing, if you ever see this puzzle, do check that it contains the limiting factor that only one item can be on the boat, otherwise the answer is just to load all three on the boat. Also that it explicitly, or strongly implicitly gives you the information that the fox will eat the chicken etc. It could be a double bluff.





© Nigel Coldwell 2004 -  – The questions on this site may be reproduced without further permission, I do not claim copyright over them. The answers are mine and may not be reproduced without my expressed prior consent. Please enquire using the link at the top of the page.
 


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