The determinant game
December 12th, 2007 ~ Posted in: Generalvia The Art of Problem Solving, let’s play a (two-person) game.
Start with a 3×3 zero matrix, and at their turn each player changes one of the zero entries to a number between 1-9. The first player’s goal is to make the determinant positive, while the second’s is to make it negative. Numbers may be used only once.
Play it a couple of times. Now analyze it!
General ~
3 Responses to “The determinant game”
December 15th, 2007 at 1:42 pm
This is similar to problem A4 of the 2002 Putnam Competition:
http://www.unl.edu/amc/a-activities/a7-problems/putnam/-pdf/2002.pdf
I haven’t yet had much time to analyze it, but it’s a pretty interesting problem!
January 3rd, 2008 at 1:12 am
[…] Determinant Game Via Alex Gittens’ blog, here’s a cool […]
January 6th, 2008 at 3:38 pm
[…] week’s question has been inspired by the Determinant Game which was posted by ChapterZero. I haven’t determined the heuristics needed to win this game, […]
This entry was posted on Wednesday, December 12th, 2007 at 6:03 pm and is filed under General. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.
Leave a Reply