In my previous post (silly carpets and the light switchers) I mentioned an interesting problem and promised to post the solution – I’m sure it was easy enough the work out especially since the title also mentioned prime and square numbers. I’ve never actually done it practically before. But for you, dear reader, I’ll go that extra mile. Really glad I did because I’ve just appreciated that that this is a really great problem for upper ks2 ( possible ks3. – what do I know?) and a fun way to rehearse those tables yet again. I wanted to video it but lack of something to fix my phone/ iPad into eluded me. Too many shots of me in my dressing gown (hey it’s the weekend, you don’t expect me to actually get dressed?) So just what is probably one of the most boring sets of photos ever- but what was strangely satisfying to do in practice. I needed an object I could turn over to signify the light being on or off. Having no plastic cups I resorted to nespresso coffee capsules which makes this the most middle class poncy maths investigation ever….in class maybe use those mini ketchup cups you get at McDonalds or biscuits like Jaffa cakes which have very different sides and which we now all know are zero rated for vat, thanks to MP Stella Creasy.

So first of all all the lights are off so my capsules are all the right way up.

Then number one switches all her multiples on – i.e turns all of the capsules over.

As every number is a multiple of one, all the capsules are turned over- all the lights are now on.

Then along comes number two and turns over all,of her multiples, making this obvious pattern.

Then number three turns over all of his, making this interesting pattern.

Number four turns over all his multiples…

And I’m losing the will to live inserting all these photos, so I will cut to the chase. Here is what it looks like after number 25 has done her switching. Drum roll please….

So the lights left on are 1,4,9,16 and 25 ( and following- I decided modelling it to 25 was quite enough) because, of course, square number have an odd number of factors whereas all the other numbers have an even number so return to their original ‘off’ state.