MathDB

4

Part of 2006 Stanford Mathematics Tournament

Problems(4)

Triple-Elimination Tournament

Source:

3/15/2010
In a certain tournament bracket, a player must be defeated three times to be eliminated. If 512 contestants enter the tournament, what is the greatest number of games that could be played?
Simiplifying a Complicated Expression

Source:

3/15/2010
Simplify: \frac{a^3}{(a\minus{}b)(a\minus{}c)}\plus{}\frac{b^3}{(b\minus{}a)(b\minus{}c)}\plus{}\frac{c^3}{(c\minus{}a)(c\minus{}b)}
Rice and Stanford

Source:

3/20/2010
Rice University and Stanford University write questions and corresponding solutions for a high school math tournament. The Rice group writes 10 questions every hour but make a mistake in calculating their solutions 10% of the time. The Stanford group writes 20 problems every hour and makes solution mistakes 20% of the time. Each school works for 10 hours and then sends all problems to Smartie to be checked. However, Smartie isn’t really so smart, and only 75% of the problems she thinks are wrong are actually incorrect. Smartie thinks 20% of questions from Rice have incorrect solutions, and that 10% of questions from Stanford have incorrect solutions. This problem was definitely written and solved correctly. What is the probability that Smartie thinks its solution is wrong?
Stanfordcollegeprobability
2006 SMT Team Round #4 - What Polynomial?

Source:

8/22/2011
Let x+y=ax+y=a and xy=bxy=b. The expression x6+y6x^6+y^6 can be written as a polynomial in terms of aa and bb. What is this polynomial?
algebrapolynomial