The “Friday Afternoon Mathematics Undergraduate Seminar” (FAMUS) is a weekly event consisting of announcements, talks, and faculty interviews. FAMUS takes place most Fridays at 3:00-4:00pm in Room 164 of the Adel Mathematics Building. Typically the first half of FAMUS consists of a talk on a mathematical topic while an interview of a faculty member takes place in the second half. FAMUS is hosted by Jeff Rushall.

Come join us for some entertaining talks! Refreshments always served.

Note that talks are listed in reverse chronological order.

**Date:** Friday, September 30

**Speaker:** Jeff Rushall (NAU)

**Abstract:** Graph labeling is a fun game played on graphs: given a specific kind of graph, and given a set of labeling rules, find a way to label the vertices and/or the edges of the graph that obeys the given rules. Some known theorems and known open problems will be presented.

The faculty guest interviewee is new faculty member Hannah Prawzinsky. [PDF of Flyer]

**Date:** Friday, September 23

**Speaker:** Jeff Rushall (NAU)

**Abstract:** The 10958 Problem involves the following puzzle: using the digits $1, 2, 3, 4, 5, 6, 7, 8$ and $9$, in that order, and using any of the standard arithmetic operations (addition, subtraction, multiplication, division, exponentiation, factorials and concatenation), what natural numbers can you build? Some answers are easy: you can build $45$ ($45 = 1+2+3+4+5+6+7+8+9$), you can build $43$ ($43 = 1^2 + 3+4+5+6+7+8+9$), and so on. Some are not so obvious, like: $10957 = (1 + 2)^(3+4) × 5 - 67 + 89$. It turns out you can build every natural number up through about $11,000$ according to these rules - except for one special integer (look closely at the talk title for a hint).

The faculty guest interviewee is Robert Buscaglia, who in addition to being interviewed will HAVE HIS HEAD SHAVEN DURING FAMUS FOR CHARITY. Others are welcome to also have their heads shaven. [PDF of Flyer]

**Date:** Friday, September 16

**Speaker:** Jeff Rushall (NAU)

**Abstract:** The talk topic this week is “The Happy Ending Problem,” so coined by Paul Erdos. This topic is a mix of math, tragedy, and a love story. The math revolves around a problem in planar geometry that involves convex polygons.

The faculty guest interviewee is Tyler Brock, who will answer a prearranged set of humorous questions and show humorous pictures from his past. In addition to being the first FAMUS of AY 2022-2023, both Math Club and the Putnam Exam will recruit from the students in attendance. [PDF of Flyer]