Each semester, the college’s math department runs a weekly puzzle competition called the Team Barge Competition. The solutions to these puzzles involve ingenuity and insight, but do not require knowledge of advanced math topics. For this reason, the competition is accessible even if you are not a math major. However, the official competition is only open to current Lafayette students.
The college’s math department will begin publishing these puzzles in 2018, so that students may participate. Current students interested in officially competing can visit math.lafayette.edu/teambarge and email Professor Jonathan Bloom at [email protected] to register a team for the spring 2018 semester. The first place team wins $750, second place team wins $600 and third place team wins $450.
Lafayette vs. Lehigh
As you know, the Lafayette vs. Lehigh football rivalry has been raging for over 150 games. This year the organizers want to up the ante! In particular, they plan to extend this rivalry to include the pre-game tailgating. For this occasion, the organizers have built a special parking lot with spaces arranged in an n X m grid. The rules for choosing a tailgating space are as follows. First, a Lafayette fan picks some (arbitrary) space S1. Next, a Lehigh fan picks some space S2 which must be adjacent (above, below, right, or left) to S1. This process continues in an alternating Lafayette/Lehigh fashion so that the Si+1st spot chosen is adjacent to the Sith spot. This process terminates when some side is unable to choose a spot. In this case that side is deemed the loser!
Depending on the values of n and m, is there a strategy by which the Lafayette side can guarantee a tailgating win? What is this strategy?