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Age 11 to 14 Challenge Level:

This problem was written by James from St Peter's College, Adelaide, Australia.

Draw a pentagon and draw in all the diagonals (lines joining the vertices not including the edges of the pentagon), how many diagonals is this?

This is called a pentagram. How many diagonals are there in a hexagram, heptagram, octagram, nonagram, decagram etc. up to a 20 sided shape.

Does any pattern occur when looking at the number of diagonals?

Why is this so?

Can you find a formula?