Each week Mondays at 6:30 in LABS 111 for recreational math and Thursdays at 6:30 in LABS 111 for math for competitions. Everyone is welcome to attend every week or just once if you want to check it out. Please reach out to a friendly cohead or advisor if you have questions.
Jason He & Raphi Kang.
Faculty or Staff Advisors:
We plan to attend the Harvard MIT Math Tournament in November! Please email any of the faculty advisor(s) or cohead(s) with questions or for more information.
List of summer math camps US (word doc)
List of summer math camps in US (pdf)
Current Problem of the Fortnight:
The Pigeonhole Principle is a simple, yet powerful mathematical principle. It states that if you have more pigeons than you do pigeonholes (places to put pigeons), then there will be a pigeonhole that contains more than one pigeon.
Problem A: Show that there are at least two non-bald people in Boston with exactly the same number of hairs on their heads.
Problem B: Five points on the surface of a sphere are chosen at random. You are asked to cut the sphere in half however you like. Show that you can always guarantee at least 4 points on one of the two hemispheres. (HINT: You can choose which hemisphere the points you are cutting through go with.)
Problem C: 27 points are arranged in three rows containing nine points each. Each point is chosen to be either blue or red at random. Show that there is a monochromatic rectangle formed using four of these points (this means all four vertices are the same color).
Solutions are due by 3:15 PM on 12/12. See Shawn with questions.