Dear Sirs: My name is Heba Hathout. I am a sophomore in high school at the Westridge School for Girls, in Pasadena, California. I am submitting an article for your consideration for the RHIT Math Journal, enclosed as an attachment. I realize, of course, that it is highly unusual for someone at my level to submit an article. However, I presented this material as a poster at the MAA Southern California Section Spring Meeting held at Caltech in March of last year, and noticed that it generated substantial interest and discussion. Therefore, I thought that the material may be stimulating for the college level. The main point of this paper is to present the technique of binomial inversion, and use it to solve a standard derangements problem. What I discovered during the meeting is that the binomial inversion technique, while obviously not new, was unfamiliar to most of the students and many of the faculty, and was greeted enthusiastically. Due to space limitations on the poster, I could not present a derivation of the formula, and hence this paper. If it is too long, I can easily skip the more familiar approaches in the first two sections, and focus only on the binomial inversion solution and formula derivation. I am calling the paper "The Old Hats Problem: Derangements and Binomial Inversion". I will include an abstract under separate cover. My advisor for this work was Dr. John Woo, a medical doctor and avid mathematician, who majored in math at Harvard, and before that was a member of the United States IMO team for two years. Below is a paragraph about me, and this work, as you requested, written in the first person: "My name is Heba Hathout, and I am currently a high school sophomore at the Westridge School for Girls in Pasadena, California. I have loved math for as long as I can remember, and hope to be enjoy its beauty always. I became interested in combinatorics as a freshman, and started investigating derangements using different techniques. With my advisor, Dr. John Woo, we developed a binomial inversion approach to tackling problems of derangments, and presented this work at the Spring Southern California meeting of the MAA at Caltech in 2002, where I was the lone high schooler presenting. That was very intimidating, but also thrilling." Sincerely, Heba Hathout email: Agraba4@aol.com -------