MathDB

1

Part of 2007 Stanford Mathematics Tournament

Problems(3)

SMT 2007 Team #1

Source:

6/30/2012
How many rational solutions for xx are there to the equation x4+(2−p)x3+(2−2p)x2+(1−2p)x−p=0x^4+(2-p)x^3+(2-2p)x^2+(1-2p)x-p=0 if pp is a prime number?
Bins of Improperly Labeled Fruits

Source:

3/15/2010
There are three bins: one with 30 apples, one with 30 oranges, and one with 15 of each. Each is labeled "apples," "oranges," or "mixed." Given that all three labels are wrong, how many pieces of fruit must you look at to determine the correct labels?
SMT 2007 Algebra #1

Source:

6/27/2012
Find all real roots of ff if f(x1/9)=x2−3x−4f(x^{1/9})=x^2-3x-4.