### DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:**
**Brian Nakamura**, Rutgers University, bnaka {at} math [dot] rutgers [dot] edu
** Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Subtraction-Division games, patterns, and self-similarity

Speaker: **Elizabeth Kupin**, Rutgers University

Date: Thursday, September 22, 2011 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

This talk will investigate a two player combinatorial game
with parameters a, b and n. The game starts at a prearranged
number n, and is a race to say the number 1. Each player, on
his or her turn, can either subtract a from the current
number, or divide the current number by b and round up. We
will look at the Sprague-Grundy function of this game, and
in particular, the sequence created by fixing a and b and
letting n vary. While this sequence is not periodic, for
many pairs of values a and b there are interesting patterns
that appear. For certain pairs a and b, we will also be able
to answer the more practical question - is there a simple
formula for who wins?

See: http://www.math.rutgers.edu/~bnaka/expmath/