MathDB

6

Part of 2006 Stanford Mathematics Tournament

Problems(4)

Really Bad Clock

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3/15/2010
An alarm clock runs 4 minutes slow every hour. It was set right 312 3 \frac{1}{2} hours ago. Now another clock which is correct shows noon. In how many minutes, to the nearest minute, will the alarm clock show noon?
2006 SMT Algebra #6 - All Values of a+b+c

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8/24/2011
Let a,b,ca,b,c be real numbers satisfying: ab−a=b+119ab-a=b+119 bc−b=c+59bc-b=c+59 ca−c=a+71ca-c=a+71 Determine all possible values of a+b+ca+b+c.
SFFT
Number of Possible Winning Scores

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3/20/2010
Ten teams of five runners each compete in a cross-country race. A runner finishing in nth place contributes n points to his team, and there are no ties. The team with the lowest score wins. Assuming the first place team does not have the same score as any other team, how many winning scores are possible?
2006 SMT Team Round #6 - Find p(2006)-q(2006)

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8/22/2011
The expression 16n+4n+116^n+4^n+1 is equiavalent to the expression (2p(n)−1)/(2q(n)−1)(2^{p(n)}-1)/(2^{q(n)}-1) for all positive integers n>1n>1 where p(n)p(n) and q(n)q(n) are functions and p(n)q(n)\tfrac{p(n)}{q(n)} is constant. Find p(2006)−q(2006)p(2006)-q(2006).
functionratiogeometric series