Lucy and Lily: A Game of Geometry and Number Theory

1. INTRODUCTION. The purpose of this article is to describe a computer game I created. I named the game " Lucy and Lily, " after my two daughters. If you want to play this game, you can find it on my website www.math.umd.edu/∼res. Some browsers have trouble with the game, but some work just fine. Many people have expressed enthusiasm for the game, and their enthusiasm has encouraged me to write this article. At some point, Daniel Allcock and Brian Conrad worked out an informal but careful analysis of " Lucy and Lily. " The several challenges I issue to the reader, during the course of the article, derive from facts that one or both of them established.