Maths Problem

A couple of weeks ago Mrs Manning (our maths teacher) gave us homework to create a starter idea for the class that we could puzzle out on the tables in L34 and L5. So far we have tested a few and I’m going to guide you through how I worked out my favourite one which was chosen by a friend.

The problem was this: we were shown a triangle and had to work out how many triangles we could see in it (the triangle is shown in the diagram).

First I looked at all the smaller triangles. I counted them: there were 16, then I realised that there were more, bigger triangles that consisted of several triangles (4). There were 7, then I looked at the even bigger triangles (made of 9 triangles) This took me a long time but I eventually decided there were only three.

Now I started adding. I got a total of 26. So I went to tell Mrs Manning my answer but then just as I got up I noticed I hadn’t counted the rim!

So after all that I think I have cracked the puzzle: the answer is 27.

Or does anyone have an alternative answer…?