Fox goose corn riddle: How to cross the river?
Farmer to cross a river with fox, goose and corn in a boat that takes at most two. Fox eats goose and goose eats corn if left alone.
Farmer can row the boat himself and doesn't need a boatman to ferry them across.
How can he cross the river with all the three unharmed in least number of trips?
Time to solve: 15 minutes.
Try to solve the puzzle. It will be worth trying and will entertain for sure.
And when you come to know the solution, puzzle your friends and seniors with this age-old classic river crossing riddle. It’ll be fun.
About the riddle
This may be the oldest riddle in this category of river crossing riddles. Many variations circulate all over the world keeping the main facts unchanged,
- One person with three items has to cross a river in a small boat,
- He can make as many boat trips as needed. No limit to number of boat trips.
- But he can take at most one of the three items in the boat along with him, and
- He cannot leave alone, say, first with the second item or second with the third item.
In our riddle, the farmer cannot leave alone the fox with the goose, or the goose with the bag of corn.
It is common sense, isn't it? In the first case, the fox will eat up the goose and in the second case, the goose will finish the corn.
Okay, now it is time to explain the solution to you.
Be prepared, we won't tell you the solution in a few words—we'll analyze the puzzle and take most reasonable decisions. This way, you will see the solution yourself.
Solution to the Fox goose corn riddle: How to cross the river?
A few months back while we were chatting with a young couple visiting our house, I offered the riddle to their 7 year old restless son.
The child and a few of the adults took up the apparently mild challenge to solve the riddle (riddles are always intriguing, isn't it?).
Next twenty minutes passed hilariously with possible solutions, queries and banters exchanged excitedly.
After a while, as it usually happens, interest shifted.
None could propose a correct solution. That is natural. We were in a group with no focused attention on solving the riddle. And all tried to solve in their usual random way.
Let's look at the riddle using logic and reason. Basically, it is a deductive reasoning based problem solving puzzle. A general name for this type of puzzles is brain teaser.
First stage analysis: Fox goose corn riddle: What is the biggest hurdle in solving the puzzle?
In any problem solving, you will automatically ask yourself this question and try to find the most suitable answer. The two hurdles in this puzzle are,
- The farmer can take at most one of his three items on a boat trip, and
- He cannot leave alone the fox with the goose or the goose with the bag of corn.
In fact, these two constraints only make the puzzle intriguing.
Second question is: Which one of these two is more important?
This is where you must use your logic based reasoning and judgment.
You may intuitively decide that the second constraint is the most important one. But why?
If the first constraint of at most 1 item on a boat trip is removed, the farmer can take all three items on a single boat trip, and the story ends. It has an important role certainly. But, you cannot increase the boat capacity.
That means, you cannot take any special action or decision using this constraint.
What about the second constraint of fox eats goose, and goose eats corn?
You decide the trips may be planned using this constraint.
For planning successful crossing, no means or choice available to you other than this constraint in a fruitful way, isn't it?
That’s why we classify this second constraint as the most important.
This is Primary barrier identification by barrier analysis.
An interesting point to remember while solving a problem,
The most important hurdle is usually also the most important help in solving the problem, if you can breakdown and use the hurdle suitably.
Second stage analysis: Fox goose corn riddle: How to breakdown and use the most important hurdle: break the chain technique
The following graphic shows who eats whom pictorially.
The fox eats the goose but doesn’t eat the corn. The goose eats corn and no way can eat the fox.
With this knowledge clear in your mind, you can now make a confident decision,
If you can plan the trips so that neither fox with goose nor goose with corn stay together on any of the two river banks, then only can you solve the riddle.
You can surely leave the fox with the corn, no harm will come, but you won’t ever allow the goose come into the company of either of the two without your presence (imagine yourself as the farmer, it will help in finding the solution psychologically).
This is what we call—the guiding strategy in solving the riddle.
And the technique of removing the middle member of the three-member chain we call as, break the chain technique.
The picture below shows the three-member chain broken,
Third stage analysis: Fox goose corn riddle: Planning the first trip
On the first trip, can you take either the fox or the corn with you?
No way. Being aware of break the chain technique and the guiding strategy, you can take only the goose in your boat on the first trip to the other bank.
This is your only choice.
After reaching the other bank of the river, naturally you would leave the goose alone on the second bank, AND return to the first bank with the empty boat.
Fourth stage analysis: Fox goose corn riddle: Planning the second trip: Point of second breakthrough
On the second trip now, you may take either the fox or the bag of corn with you. If you think for a moment, you realize that both plans of action are equivalent to each other.
Let's assume you have taken the fox with you on the second trip.
This decision is easy to take.
But what will you do after reaching the opposite bank? You will surely leave the fox on the opposite bank, there is no point in returning with the fox again. This also is a certain decision.
But is that all? This is the point of second breakthrough, or the turning point in solving the riddle.
As you can't leave the goose with the fox alone, you will return WITH THE GOOSE, keeping the chain broken this time as well.
And this choice is the only one left with you. It's logical.
Fifth stage analysis: Fox goose corn riddle: Action after reaching the first bank, planning the third and fourth trips and final solution
Maybe by now you have understood the logical reasoning and should be able to go through the next actions to finally transport all three of your assets safely to the opposite bank.
Without reading further, try to complete the rest of the steps.
Obviously, after reaching the first bank with the goose, you cannot take the bag of corn together with the goose, or, you cannot take the third trip again with the goose.
The only choice that you have is to leave the goose on the first bank and take the bag of corn, cross the river with the bag still ensuring that the three-member chain remains broken.
When reaching the opposite bank now, you will deposit the bag of corn safely with the fox and return to the first bank to take the lonely goose with you on the fourth trip.
At the end of the fourth trip, you will get off the boat with the goose, and you have completed your job of crossing the river with three assets successfully and safely.
The pictorial representation of the four trips is shown.
Now that you know ins and outs of the riddle, and it would be great fun to pose it to anyone—your friends or seniors, and enjoy solving it together.
End note
See that at no point in analyzing and taking decisions, we have made any guesses. Like clockwork, solution is reached step by step systematically. This way of thinking should be of great help in solving large problems.
This is systematic problem solving, and the techniques used are primary barrier identification and question analysis answer or QAA technique in short.
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