### 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:**
**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

Abstract:

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/