Try your hand at this puzzle!

Written by Emilyn who is a Science Educator at Science Centre Singapore.

How many activities can draw a cult following because of their educational nature? Only a handful, I think, and among the well-loved ones are puzzles. We solve puzzles to train our minds, run competitions on them or just for plain recreation and relaxation. Big companies like Google and Microsoft use puzzles as interview questions. In this age of technology where creativity and computational thinking matter, it is more important to understand how you think about framing and solving problems.

Puzzles in Lessons

Here in Science Centre, such puzzles are employed in our lessons, namely, Techno Maths Mania (for novice) and Brains over Brawn (for the brave souls).  These two can be taken in any order. For a notoriously difficult subject as computing, puzzles provide an accessible, collaborative, engaging and visual platform for the learners to understand the strategies that can be employed. Following are some of the students working in teams and squeezing their creative juices out to come up with a solution.

Students from Bedok South Secondary School

Students from Yuvabharathi International School of Singapore

A Classic Puzzle

Let’s refer to a classic example. The puzzle below can be traced back to year 781 AD, by an eighth century English scholar, Alcuin of York, when he was invited by Charlemagne to teach at the palace school in Aachen. Now, this puzzle is used by textbooks to introduce the concept of artificial intelligence (AI)! As one of the objectives of the lessons is for the students to learn how to express their thinking in mathematical terms, the solution must be comprehensive, logical and knowledge is transferable.

A farmer has to take a wolf, a goat, and one big head of cabbage across a river. There’s a rowboat that has enough room for the farmer plus either the wolf or the goat or the cabbage (obviously, only the farmer can row the boat). If he takes the cabbage with him, the wolf will eat the goat. If he takes the wolf, the goat will eat the cabbage. Only when the farmer is present are the goat and the cabbage safe from their enemies. How should the farmer take the wolf, goat, and cabbage across the river?

This puzzle will likely ring a bell. Most of us might have encountered this problem before but how did we go about solving it? We probably just verbally communicated the answer but in the world of computing, all states must be traceable and all conditions covered. Approach the problem in a mathematical way and you’ll realise how this found its way in AI. After thinking about a solution, get a pen and paper, lay your thoughts out in terms of a tree consisting of nodes and edges (refer to diagram below) where the initial state (top oval) is having all characters on left side of the river and final state (bottom oval) is when they are all safe on the right side of the river. You can draw a divider, like ||, to represent the river.


A Tree  Consisting of nodes and edges

Once you note down your thinking this way, you’ll notice that there are two possible solutions to reach the final state. So that means somewhere in the middle, it can branch out and converge to the end. In your solution, also include the illegal, invalid or unsafe states in red, just like the example below:


An unsafe state where the goat and wolf are left alone

Now sit and think for a while… Got a solution? Share it with us by commenting it below (you can draw by hand and take photo). We would love to see it!

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