This problem did prove to be tricky. Very tricky! There are many triangles embedded within the large one. The key to discovering the total number of triangles is to have a systematic method of looking at each of the separate triangular pieces of the whole triangle diagram. Many people worked in a very well thought out and organised way on the problem and provided clear and full explanations of their strategies for approaching the task. It was a challenge to make sure you didn't count the same triangle twice.

What was interesting was that, despite using similar ways to tackle the problem, there was almost no agreement on the answer!! The numbers given ranged from 20 to 26. Did anybody find more than 26 triangles? How could you check the solutions to prove your own answer? Here are some of the strategies used.

Marion Sanders, aged 9, from Tattingstone School labelled each vertex in the triangles and then was able to name each individual triangle to help her keep track.

A couple of groups of pupils from Brooklands C.P. School in Brantham, Suffolk also put a lot of work into their solutions. Guy W. and Adam O. worked together as did Lynsey Dearling, Olivia Langdown, Annabel Leech and Crystal Wosko. The girls described their practical strategy: First we cut out 13 whole triangles and left one triangle whole. Next we cut out the triangles we could see. Then we looked deeper into the triangles and counted them.

The final step was to name the different types of triangles and reveal how many of each there were. Joanne Langford from Moorefield Junior School, Hazel Grove in Stockport used a technique similar to the Brooklands pupils. Yoonha Lee and Elizabeth Ward from Mayfield Primary School in Cambridge also sent their solution to Tricky Triangles. They counted all of the triangles they could make with one triangle, then two, and so on until they decided they had made all of them.

Can anybody convince us why their answer was correct and where other people might have slipped up?