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Triangles Within Pentagons

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Having identified the rule is it possible to work backwards and reconstruct pentagons using the triangular numbers?

This problem builds on the work of the three problems "sequences and series ", "triangles within triangles " and "triangles within squares ".

There are many more patterns and relationships involving triangular numbers and some experimentation could result in some pupil generated discoveries.