Brian Pinsky, Rutgers University

Abstract

I wanted to give a talk called "facts one usually learns in the first day of a class on coding theory", but that didn't seem compelling.  Fortunately, roughly half of the math puzzles one gives to high schoolers are really just thinly veiled coding theory problems.  So, in this talk, I will give a bunch of fun math puzzles to give to high schoolers.

However, unlike high schoolers, grad students don't feel satisfied with a problem until it's so general it hurts their brain.  To that end, I will provide a massive heap of definitions, at the root of which is algebra you forgot years ago. 

For those who like injuring themselves before the talk, consider the following problem: There are 11 coins, of which at most 2 are counterfeit and have non-standard weight (lighter or heavier).  If given a 2 sided balance that breaks after 5 uses, can the counterfeit coins be identified?  If this answer doesn't surprise you, I will convince you that it should.