An Infinite Limit of Conway’s Soldiers (Jack McKenna)

17:00, June 5, Microsoft Teams meeting

Abstract: This talk will extend the treatment of the Conway’s Soldiers game on an infinite chequerboard which I briefly described in the PGR talk two weeks ago (though it’s not necessary to have attended that one!). I’ll review the description of Conway’s Soldiers in the plane and the proof that no finite number of moves can bring a chequer to the fifth row above the starting position. I’ll then describe a suitable infinite limit of the game in which a “converging infinite sequence” of moves allows us to get exactly to the fifth row, but no further.