Empowering Young Mathematicians: From Sprouts to Solutions

This half-term, members of the Inspiration Trust maths team visited Year 7 students across the East Maths Community to deliver fantastic enrichment lessons on Graph Theory and Topology - topics that mathematicians would normally need to wait until university to experience. 

Tasked with solving the seemingly unsolvable 'Three Utilities Problem', students were constrained by the annoying 2-dimensionality of their paper and mini-whiteboards when trying to get everything connected without any lines crossing. 

To prepare for this challenge, students got acquainted with mechanics of Graph Theory by learning to play the game of 'Sprouts' (a quick two-player strategy game, the next level up from Noughts and Crosses). This equipped students with the notation and know-how to try 'Untangling Graphs', to determine if they are planar (i.e. drawn without any lines crossing). 

Finally, higher-dimensional manifolds of Topology enter the fray, where the distinct feature of torus and torus-like objects (e.g. donuts, rubber rings, even mugs!) make a solution to the 'Three Utilities Puzzle' possible. 

HINT: What do they all have in common? 

Relieved of the constraints of 2D, students were delighted by the extra freedom of movement the toroidal wooden rings gave them and kept their completed puzzles as a symbol of their mathematical prowess. 

We thoroughly enjoyed visiting the schools involved in the programme and look forward to seeing what they can achieve in their Maths Clubs moving forward.