Wednesday, August 17, 2016

Games@Dal 2016: Tanya talks about Cookie Monster Games

Games@Dal 2016 talk: "Cookie Monster Plays Games" - Tanya Khosanova w/Leigh Marie Braswell, Eric Nie, Alok Puranik, Joshua Ziong, and Dhroova Aiylam

Tanya Khovanova shared some work with a bunch of high schoolers (whoa!) on patterns in Cookie Monster games.  Cookie Monster games are Nim games where k sticks (cookies) can be removed from multiple heaps.  Each ruleset has a different restriction on which sets of piles can be removed from.

She and her students considered rulesets where you can take from...:
  • No restriction
  • One-or-all piles
  • One-or-two piles
  • Any consecutive piles (assuming the piles are in a list)
  • One or two consecutive piles
  • Any set of piles including the first jar
  • Any odd number of piles.  (It turns out that the P positions are the same as in Nim!)
  • Any set of piles except all of them.
  • ... and more!

In one of these games, she noticed a surprising correlation with an automaton problem!  A sequence of the number of P positions is related to the number of new cells born from the Ulam-Warburton automaton.  She then looked more closely at other relationships to automaton!

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