The River Crossing Puzzle

Have you ever heard of the man who needed to get a chicken, a fox, and a sack of corn across the river? He has a small boat, only big enough for himself and one other item. The problem is he cannot leave the fox alone with the chicken, and he cannot leave the chicken alone with the corn. He must find a solution to get everything across the river safely and intact.

This is a classic puzzle that often introduces people to the idea of problem solving. We must find a solution to the puzzle, whilst respecting the constraints set before us. Before we break down the solution, feel free to attempt solving this one yourself, and come back to see if you were right.

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Understanding the task

We can break down the rules and constraints of the puzzle into bullet points. This may seem obvious, but it will be a useful reference for us when we are later solving the problem. Let’s write them down:

• We must get three items across the river 🦊 🐓🌽
  • We can think of this as moving from A to B
• The boat can only hold the man and one other item 🚣
  • We can choose, each time, which item goes in the boat
• If left alone:
  • The Fox will eat the Chicken 🦊🐓
  • The Chicken will eat the Corn 🐓🌽
• All three items must make it from A to B safely and intact 🆗
• Assumptions:
  • We are allowed to take as many trips as possible to complete the task
  • We must use the boat to move, or carry the items, across the river

The first move

Let’s take a look at our possible options for the first move.

1. If we take the Fox across the river first, then the Chicken will be left alone with the Corn ❌
2. If we take the Chicken across the river first, then the Fox will be left alone with the Corn
3. If we take the Corn across the river first, then the Fox will be left alone with the Chicken ❌

Of the three possible options, we can see that option 1 and 3 will break the constraints of our puzzle – resulting in one of our items being eaten.

• Therefore, we can choose option 2 as our first move; taking the Chicken across the river first (to B), because the Fox can safely be left alone with the Corn (at A) ✅

Making progress

Now that we understand the task at hand and the constraints of the puzzle, let’s try to make some progress and move the other items across the river

Let’s take a look at our possible options for the next move:

1. If we take the Fox across the river next, then the Fox will be left alone with the Chicken when we go back for the Corn ❌
2. If we take the Corn across the river next, then the Chicken will be left alone with the Corn when we go back for the Fox ❌

You’ll notice here that neither of these options will help us complete the task, because we can’t leave the Chicken alone with the Fox or the Corn when we go back to get the final item.

Let’s think one step ahead, and consider the constraints of the puzzle:

• If we take the Fox or the Corn across the river (to B) we cannot leave either of them alone with the Chicken
  • Therefore, we can take the Chicken back with us across the river (to A), leaving the Fox or Corn alone on the other side (at B) ✅

This may not seem like we are making any progress, but we are using the constraints of the puzzle to our advantage. We were not told that we cannot bring an item back across the river, from B to A, and we know that we can make as many trips as necessary to complete the task.

Continuing the sequence

We’ll say that we took the Fox over to the other side (at B), before bringing the Chicken back with us across the river (to A).

Let’s continue with the rest of the sequence:

• We’ll leave the Chicken (at A), then take the Corn across the river (to B)
  • We can leave the Corn alone with the Fox (at B) ✅
• We can go back across the river (to A), then take the Chicken across the river (to B)
  • This will mean that the Fox, the Chicken, and the Corn will have all made it across the river (to B), and we are there to stop anything from being eaten ✅
• Mission Accomplished 🎉

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Conclusion

If you were able to solve this puzzle by yourself, then well done! If you needed to follow the guidance, then I hope this was useful and that it gave you an insight into how you can think about puzzles – by understanding the constraints and making progress to solve them

Are there any more puzzles that you would like to see broken down?

And, as always, take it easy,

Nathan 🌱

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