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## 'Let's Investigate Triangles' printed from http://nrich.maths.org/

We had a few suggestions as to what sould be done with these strips. I've chosen three from pupils of very different ages.

Matthew

Solution: $1$ green and $2$ yellow strips

Explanation: because the green strips have $6$ holes and the yellow strips have $3$ holes and so the green strips don't have enough holes for two yellow strips together to make a triangle.

Zareah

Well, the three strips that can't make a triangle are the green, the yellow and the black because the green strip is too long to connect the yellow and black. Furthermore, you can also make a triangle with it if you space it out properly.

Oleg

In total, there $4 \times 4 \times 4 = 64$ possible combinations of strips. We picked one of the four strips, then pick again two times and make a triangle of them. But Green + Yellow + Yellow makes a degenerate triangle, that looks like a line.

This is an interesting argument but I think Oleg has counted lots of triangles more than once when they are essentially the same.

Can you see how he has done that?

Perhaps you can offer us a different solution?