# Conundrum: September 2013: Welcome back, Welcome to the Major

Math Puzzles / Contests at Williams

Lots of opportunities for math puzzles and contests, including

• Weekly Math Puzzle Night Dinners
• Monthly Math Conundrums (first one below)
• The Putnam Exam (early December — cash prizes!)
• The Green Chicken Contest (at Middlebury this year)
• Mathematical Contest in Modeling
• Project Euler

Contact Professors Miller ([email protected]) and Stoiciu ([email protected]) to be added to the email list for updates.

1st Conundrum: Math/Stats is Infectuous

The following is a standard problem, rephrased. Consider an n x n grid (so there are n2 squares). Color people purple if they’re a math/stats major, and (a sad) blue otherwise. Once you’re a math/stats major, you stay a math/stats major. If your square borders two math/stats majors, you become a math/stats major. In the picture below, in the next turn three people join the major, in the turn after that 1 more, then 1 more the next time, after which our major stops growing. Prove that if we start with n-1 majors, no matter how cleverly we place them, there will always be at least one person who doesn’t major in math/stats; however, prove that if we start with n math majors then it is possible to place them in such a way that everyone ends up joining the major!