Problem Solving Series: The Escape

Challenge yourself to a problem solving task!

In this series one of our teachers works through a problem solving task showing you how they would solve it and common misconceptions students have when solving it. Try solving the problem on your own first before watching the solutions in the video.


For this week's problem we are taking on a more challenging task - The Escape from NZ Maths

Can you figure out when the prisoner can escape?

Watch the full video of how we work through The Escape problem. Watch at your own pace and pause when you need to. Did you use the same strategies or do something different?

The first important step is figuring out what is the important information in the question. What do we need to figure out and what information do we already have? At this point you can start to think of what strategies you might use to solve this problem.

We started with finding common multiples of 1, 2, 3, 4 and 5 because this is when the guard will return. To do this we have written out the multiples of these numbers, using a counting up strategy. As you work through the problem you may find it useful to write out the multiples to find a common multiple as we have in the following video. We haven’t written out the multiples of 1 and 2 because we know that both of these factors will fit any even number.

Once we found that 60 was our lowest common multiple, we knew how long we had until the guard would come back. Then we moved on to find out at what time the prisoner could escape through each laser. We started by looking at Laser 3, which goes off every 5 minutes. Next we looked at Laser 2, which goes off every 2 minutes. By doing this we can narrow down the possible times each laser can go off. We continued in this manner, next looking at Laser 1, which goes off every 3 minutes, then Laser 4 and finally Laser 1.

Using all of this information we can finally answer the questions

  • Can the prisoner escape without the alarm in the corridor going off?

  • If he can escape, how many minutes should he wait before passing Laser One?

  • How much time will he have after passing Laser Five before the guard raises the alarm?

We hope you enjoyed working through this problem with us this week. Follow along with this series to find more problem solving tasks to challenge yourself and practice your maths skills.