River crossing puzzle - farmer, fox, goose, and a bag of corn
A farmer is to cross a river with a fox, a goose and a bag of corn in a boat that can carry at most two in a trip. He cannot leave alone the goose with the fox or the bag of corn with the goose. If he does, the fox will eat up the goose, or the goose will finish the corn.
He 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 minimum number of trips?
Recommended time: 15 minutes.
Try to solve the puzzle. It will be worth trying and a lot of fun without any doubt.
And when you come to know the solution, puzzle your friends as well as seniors with this age-old classic river crossing puzzle. It'll be fun.
About the puzzle
This is perhaps the oldest puzzle of this category of river crossing puzzle. 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, there is 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, the most interesting part,
- He cannot leave alone, say, first with the second item or second with the third item.
In our puzzle, 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 quickly—we'll analyze the puzzle and take most reasonable decisions and in the process you would see the solution yourself.
Solution to the river crossing puzzle: farmer, fox, goose and a bag of corn
A few months back while we were chatting with a young couple visiting our house, I offered the puzzle to their 7 year old restless son.
The child as well as a few of the adults took up the apparently mild challenge to solve the puzzle.
Next twenty minutes or so 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 in solving the puzzle. And all tried to solve in their usual random way.
Let's look at the puzzle 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: Question to answer: What is the biggest hurdle in solving the puzzle?
In any problem solving, you would automatically ask yourself this question and try to find the most appropriate answer. The two hurdles in this puzzle are,
- The farmer can take at most one of his three items in one 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 or hurdles are what makes the puzzle a puzzle.
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 in a boat trip is removed, the farmer can take all three items in a single boat trip, and the story ends. It has an important role certainly. But, you cannot increase the boat capacity in any way. 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?
At this point, you may feel that you should be able to plan the trips by using this constraint. You see, for planning successful crossing, there is no resource or option 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 constraint.
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 resource or help in solving the problem, if you can breakdown and use the hurdle suitably.
Second stage analysis: 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 puzzle.
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 puzzle.
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,
Right now, break the chain technique seems to be the only way to control the worldwide pandemic. It is easy to say, but it needs very detailed and determined plan and action to effectively break the chain and keep it broken.
Third stage analysis: planning the first trip
In 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 in the first trip to the other bank.
This is your only option.
After reaching the other bank of the river, naturally you would leave the goose alone on the second bank, AND return back to the first bank with the empty boat.
Fourth stage analysis: planning the second trip: Point of second breakthrough
In the second trip now, you may take either the fox or the bag of corn with you. If you think a bit you would realize that both plan of actions are equivalent to each other.
Let's assume that you have decided to take the fox with you on the second trip.
This decision is easy to make.
But what would you do after reaching the opposite bank? You would surely leave the fox on the opposite bank, there would be no point in returning with the fox again. This also is certain decision.
But is that all? This is the point of second breakthrough, or the turning point in solving the puzzle.
As you can't leave the goose with the fox alone, you would return back WITH THE GOOSE, keeping the chain broken this time also.
And this is the only option left with you. It's logical.
Fifth stage analysis: Action after reaching the first bank, planning the third and fourth trips and solving the puzzle finally
Most probably, 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 option 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 back to the first bank to take the lonely goose with you on the fourth trip.
At the end of the fourth trip, you would get down 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 below.
Now that you know ins and outs of the puzzle, and it would be great fun to pose the puzzle to anyone - your friends or seniors, and enjoy solving it together.
Observe that at no point in the process of analyzing and taking decisions, we have made any guesses. Like clockwork, solution is reached step by step systematically. This is a way of thinking and helps a lot when solving large problems.
This is systematic problem solving and the techniques used are primary barrier identification and question analysis answer or QAA in short.
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