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Grace and Brittany from Stradbroke Primary both made the problem simpler to start with (this is often a good way of starting a problem, so good thinking!). Grace wrote:


$1$ triangle makes $1$ shape
$2$ triangles makes $1$ shape
$3$ triangles makes $1$ shape
$4$ triangles makes $3$ shapes
It was hard to spot the ones that were the same. I drew them on a piece of paper to make it easier to check them.

Jonathan from Brick Street Public School explained how he found the three different ways for 4 triangles, starting with the shape made from three triangles:

There are five sides to put the fourth triangle in, but there are only three different sides to put the fourth triangle in because two sides make the same shape.

Here is a picture of the three shapes that Jonathan sent:


three different ways to put four triangles together