You might feel left in the dark with this week’s tricky little problem, but we’re here to shine a light on how to get your class to switch on their investigation skills.
This #MondayMaths problem is a variation on a classic: whether we’re looking at a hundred lamps or a thousand doors, the solution is surprisingly simple! It will be particularly topical for Year 8 classes who will be looking at factors this term.
If you’re using this in a lesson, start by letting students explore this problem without further guidance and observe the strategies they construct. It will quickly become clear that this problem is a pretty complicated process to unpick:
‘The first person turns on every light, and then the second person flicks every other switch, so they’re turning off every second light. OK, so then the third person flicks every third switch and if it’s off they switch it on, but if it’s already on they switch it back off again…!’
Scaling it down
You can start smaller to model the problem. If students reach a hair-pulling stage, ask them to look at a smaller number of lights and people. Let’s say ten of each.
They can then spot a pattern in this simplified arrangement of lights and that the remaining lit lamps are a particular type of number. If they continue to explore a larger number of lamps, will this pattern continue?
In this ten-lamp model, encourage students to follow the journey of two particular lamps: one lamp that ends up lit and another that ends up dimmed. Which particular people turned the lights on and off along the way? Was it an even number of people or an odd number of people? Why do some of the lamps get switched an odd number of times?
Once students have that light bulb moment, they will realise just how elegant a solution this problem has!
A versatile puzzle
A simplified version could well be used as a depth task in Years 5 and 6 as they will have recently got stuck into factors in Autumn 1 and explored this topic using Factor Bugs to find all the factors of a given number.
Let us know what your class thought of this week’s puzzle. The answer will be posted on Thursday on our Twitter page.Back to news list Next article