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Concord Academy

Math Club

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DESCRIPTION

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.

 

Forum:

http://vbulletin.concordacademy.org/...search-Society

 

Student Officers:

Jason He & Raphi Kang.

 

Faculty or Staff Advisors:

Shawn Bartok

 

Recent work:

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.

 

Resources

List of summer math camps US​ (word doc)​​​

List of summer math camps in US (pdf)

 

Current Problem of the Fortnight (POF):

Sprouts is a two player game that begins with n spots on a sheet of paper.  Each turn a player must draw a line that connects two different spots (or a line that connects a spot to itself, like a loop) and then draw a new spot on the freshly drawn line.  The restrictions on new lines are:

  1. The line may have any shape but it must not cross itself, nor cross a previously drawn line, nor pass through a previously made spot.
  2. No spot may have more than three lines emanating from it.

Players alternate turns until a player can no longer draw a line that follows the above rules.  The last player to actually draw a line is the winner.  Below is an example game played by starting with only 2 spots that ends after 5 new lines have been drawn.  New lines and spots are shown in red.

sprouts.png

The Question:  If the game starts with 3 spots, then what is the greatest number of lines that can be drawn before the game is over?  Come up with a conjecture (hypothesis) for the general case when there are n spots to start.

Solutions are due by 3:30 PM on 10/9.  Please direct all solutions to Shawn Bartok (MAC 212).

BONUS:  Formulate a strategy for perfect play (this means a strategy that will always result in a win).