Explore the triangles that can be made with seven sticks of the
Using a loop of string stretched around three of your fingers, what
different triangles can you make? Draw them and sort them into
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
We had a few suggestions as to what sould be done with these strips. I've chosen three from pupils of very different ages.
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.
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.
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?