By Doron Zeilberger

Delivered Jan. 29, 2015

Videotaped lecture:

[This lecture was delivered on Jan. 29, 2015 at the Rutgers University Experimental Mathematics seminar organized by Matthew Russell and Doron Zeilberger.]

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

Acknowledgement: The video was filmed and uploaded to vimeo by Matthew Russell. It was uploaded to YouTube by Edinah Gnang.

Personal Journal of Shalosh B. Ekhad and Doron Zeilberger