Equilateral triangles: 4
Isosceles triangles: 3,3,4 - 3,3,5 - (3,3,6 gives a straight line); 4,4,3 - 4,4,5 - 4,4,6; 5,5,3 - 5,5,4 - 5,5,6; 6,6,3 - 6,6,4 - 6,6,5
Scalene triangles: 3,4,5 - 4,5,6 - 3,5,6 - I make that 18 altogether.
Solutions prior to Dec 2012
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 pick one of $4$ strips, then do it again $2$ times and make a triangle of them. But Green + Yellow + Yellow make degenerate triangle, that looks like a line.
This is an interesting argument but Oleg has counted lots of triangles more than once when they are essentially the same. Can you see how he has done that and offer us a correct solution?