The tricky river crossing puzzle of two pigs and two hens crossing a river in an automated boat
Can you solve this tricky river crossing puzzle in 15 minutes? 2 pigs and 2 hens to cross a river in an automated boat that starts automatically. Read on...
Two pigs and two hens must cross a river on as few trips as possible. The boat to be used for crossing starts automatically and reaches the opposite bank when at least one of the four comes aboard.
The only constraint is—being extra heavy, the two pigs cannot use the boat together for crossing—it will sink.
Time to solve: 15 minutes.
We’ll analyze the puzzle and take the most reasonable decisions for solving the puzzle.
Solution to the Tricky river crossing puzzle of 2 pigs and 2 hens crossing a river
Usually we try to approach solving a problem or puzzle in a random way. That’s the natural tendency. Try to avoid it and think analytically and systematically.
Let’s look at the puzzle using logic and reason, step by step.
First stage analysis: 2 pigs and 2 hens crossing a river: Which is the biggest hurdle in solving the puzzle?
In solving any problem, you will usually ask yourself this question and try to find the best answer. Though only one constraint is mentioned, there is a second implicit constraint—the boat won’t start when no one is in it. So the puzzle has two hurdles or constraints,
- The boat won’t start and move automatically when empty, and,
- The two pigs cannot board the boat together, but one pig and one hen or two hens are allowed on a trip.
Which one of these two constraints is more important?
The first constraint is a basic bottleneck and to ensure that the boat moves, you will always take care to have at least one of the four to be on board. That much and not more you can do with this constraint.
What about the second constraint? Oh yes, because of this constraint, you can think of a number of different combinations of passengers on a trip. And surely you feel, you would reach the solution if you think reasonably with a cool head.
That’s why we classify this second constraint as the most important constraint.
An interesting point to remember while solving a problem,
The most important constraint is usually the most important help in solving the problem, if you can analyze and use the constraint suitably.
Second stage analysis: 2 pigs and 2 hens crossing a river: How to use the most important constraint in solving the puzzle
Follow the reasoning steps carefully.
Step 1. As the two pigs may not cross together, you’ll focus on the problem of how the two pigs will cross. What you have done is—you have identified the core problem to solve.
Step 2. A natural conclusion follows—when a pig or hen is left on the first bank and the boat is on the opposite bank, a hen must bring it to the first bank, isn’t it?
The must do action is then—in every return trip there must be one hen in the boat. This is the key conclusion or key pattern identification.
This is what we call—the guiding strategy in solving the puzzle.
Okay, with these two clear conclusions, you could now plan for the first trip.
Third stage analysis: 2 pigs and 2 hens crossing a river: Planning for the first and the subsequent trips for final solution
Step 3. To minimize the number of trips, two of the passengers must cross on the first trip. Let’s assume, you have decided that the one hen and one pig cross the river on the first trip.
Step 4. Now there is only one option for the return trip—the pig leaves the boat for the opposite bank and the hen returns to the first bank.
Step 5. Second trip: You decide that one hen and the second pig take the second trip. In case of one passenger on the second trip, number of trips will be more. So, there must be two passengers on the second trip with one left on the first bank, and one pig left on the opposite bank. The one left on the first bank may be a pig or a hen.
Final step 6. Second return trip followed by the 3rd and final trip to the opposite bank: As before, the pig is left on the opposite bank and the hen brings back the boat to the first bank to take the hen left there in the final trip to the opposite bank.
In summary, to transport each pig, one trip is required and for the two hens one more trip is needed. 3 trips are the minimum—in two trips, all cannot be transported across, and in each trip there must be two on board.
The pictorial representation of the three trips is shown.
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 systematic and analytical way of thinking is a great help in solving large or small problems.
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