The determinant game
via 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!
Possibly relevant posts:
- On Being (or becoming) an expert (8/15/2006)
- arrogance, mine (p2) (8/23/2003)
- One interesting corollary of our error bounds (10/21/2008)
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!
Comment by rod. — 12/15/2007 @ 1:42 pm
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