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Two pigs and two hens crossing river puzzle

Two pigs and two hens to cross a river in an automated boat

two pigs and two hens crossing river puzzle


The puzzle

Two pigs and two hens must cross a river in 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.

We recommend no specific time duration to solve the puzzle.

Let's assure you that this is an easier puzzle than the previous river crossing puzzle by a farmer.

We'll analyze the puzzle and take the most reasonable decisions for solving the puzzle.

Solution to the puzzle: two pigs and two hens crossing a river in a boat

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: which is the biggest hurdle or constraint in solving the puzzle?

In any problem solving, you would usually ask yourself this question and try to find the best answer. Though only one constraint has been mentioned explicitly, 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, namely,

  1. The boat won't start and move automatically when empty, and,
  2. The two pigs cannot board the boat together, but one pig and one hen or two hens are allowed in a trip.

The puzzle is puzzling because of these two constraints only!

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 in 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 also the most important resource or help in solving the problem, if you can analyze and use the constraint suitably.

Second stage analysis: How to use the most important constraint in solving the puzzle by reasoning step by step

Follow the reasoning steps carefully.

Step 1. As the two pigs are not allowed to 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 thenin 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 would now be able to plan for the first trip.

Third stage analysis: 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 in the first trip. Let's assume, you have decided that the one hen and one pig cross the river in 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 one pig take the second trip. In case of one passenger in the second trip, number of trips will be more. So, there must be two passengers in 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 below.

final-solution-schematic-two-pig-two-hens-puzzle

End note

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 systematic and analytical way of thinking and helps a lot when solving large or small problems.


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