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The Angel and Devil Problem

I co-authored this expository paper with my classmate Tej Nadkarni at Euler's Circle in the fall advanced class on Combinatorial Game Theory. The Angel and Devil problem is a famous challenge in the mathematics community, first proposed by John Conway.

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Proof for k = 1

We independently wrote an algorithm that conclusively proved that the Devil wins the case of k = 1. The above is the diagrammatic representation of our algorithm on a 55 x 55 grid. 

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Proof for 'fools'

We summarised existing proofs of various fools (Angels of limited power) and the strategies the Devil may use to defeat them. This proved that an Angel of k > 1 must follow a counter-intuitive strategy to win. 

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Blass Conway Diverting Strategy

This theorem generalises all the proofs for the various 'fools' within one mathematical statement, a roadmap for the Angel to create an ideal winning strategy. 

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