Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

Matthew Russell, Rutgers University, russell2 {at} math [dot] rutgers [dot] edu)
Doron Zeilberger, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Guess and Check!

Speaker: Doron Zeilberger, Rutgers University

Date: Thursday, January 29, 2015 5:00pm

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


Alice and Bob have together ten apples. Alice noticed that she has two more apples than Bob. How many apples do they each have? The `clever' (but actually stupid) way to do is to solve the algebraic system of two equations and two unknowns A+B=10, A-B=2. The `dumb' (but really better) way would be to try out A=5,B=5 (no good), A=6, B=4 (yea!, we got it!), A=7, B=3 (no good), ..., A=10, B=0 (no good).

I will describe how, in contemporary enumerative combinatorics, `naive' `Guess and Check' leads much faster (and I dare say, more elegantly!) to the solutions of many combinatorial problems than more `sophisticated' and `advanced' methods.

See: http://www.math.rutgers.edu/~russell2/expmath/