# Kickoff Party 2016!

Today marked the beginning of a new year for the BCMS!

In case you missed it, we talked about the upcoming events for the year, Dawei gave an awesome presentation on flat surfaces, and we had a lot of pizza (nobody seemed to know what type one of the pizzas was… maybe eggplant, but we’re not entirely sure).

### Some Upcoming Events for the Year:

Department Tea

• Time: Wednesdays 4-5
• Place: Maloney faculty lounge
• Who: Anybody and everybody.

Introduction to $\LaTeX$

• Time: September 21st at 5:30 pm
• Place: Maloney 560
• Who: Anybody new to LaTeX (i.e. are you in Intro to Abstract?) or anyone who wants to brush up on their typesetting skills

Career Panel

• Time: October 13th at 5:30pm
• Place: Higgins 310
• Who: Anybody who wants to learn what math majors can do after college

Piersquared Tutoring

• Details TBD
• Talk to Chris Ratigan

Putnam Problem Solving Group

• Time: Wednesdays (to be confirmed)
• Place: Maloney 560
• Who: People who like fun, math, and fun math

Movie Night

• Time: later in the semester
• Movie suggestions welcome

### Problems That Were On The Board Today:

1.  You pick up a meter stick with 100 ants on it. Each ant walks 1 cm/s toward an end of the stick, and it reverses direction any time it encounters another ant. What’s the longest amount of time you’d have to wait for all ants to fall off of the end of the stick?

2.  Start from a place on the earth’s surface, travel south for 100 miles, east for 100 miles, and finally north for 100 miles and you get back to your starting point. Where did you start?

3.  How do you apply $+, -, \cdot, /, (, )$ to {3, 3, 8, 8} to get 24? Each number can only be used once (for example with {2, 2, 8, 8} we have (2 + 2) * 8 – 8 = 24).

4.  For what n, is n! equal to the number of seconds in 6 weeks?

5.  Let f be a real-valued function on the plane such that for every square ABCD in the plane, $f(A)+ f(B)+ f(C)+ f(D) = 0$.  Does it follow that $f(P) = 0$ for all points P in the plane?

6.  Show that there exists a convex hexagon in the plane such that: (1) all its interior angles are equal and (2) its sides are 1,2,3,4,5,6 in some order

7.  Show that every even integer greater than 2 can be expressed as the sum of two primes (again, if you solve this question, make sure to let me know so we can write a paper together)