MATHCOUNTS Mini - September 2009 Part 2
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Uploaded by mathcountsfdn on Sep 9, 2009
This is Part 2 of a video that focuses on MATHCOUNTS State Sprint Problem #14. Please visit www.mathcounts.org to view the video in higher resolution and to download the corresponding activity sheet.
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I used casework here because it's a strategy that most MATHCOUNTS participants, many of whom won't recognize what "8 choose 2" means yet, can use to approach and solve the problem. It's also the way one might approach this problem and discover the "dividers and dots" strategy, as well as various combinatorial identities. But, yes, for the experienced students, that would be the faster way to go, and your approach is a particularly insightful application of "dividers and dots"!
ArtofProblemSolving 11 months ago
why would you use casework for this problem? I believe there is an easier way.
Use dividers and dots. You have nine dots (as they must add up to nine) and two dviders (as you need to dividers to divide into three partitions). You then have 8 chose 2 = 28 total ways place the dividers in the gaps (aka roll a nine), but we cannot roll 1-1-7, 1-7-1 or 7-1-1, so 28-3 = 25, and then 25/6^3 = 25/216.
P.S. Big fan! Own lots of your books, so thanks!
mexicanmansam 11 months ago
ur funny....tnx...this is helpful for my competition
telle121 1 year ago