MathDB

8

Part of 2007 Stanford Mathematics Tournament

Problems(3)

SMT 2007 Team #8

Source:

6/30/2012
A 1313-foot tall extraterrestrial is standing on a very small spherical planet with radius 156156 feet. It sees an ant crawling along the horizon. If the ant circles the extraterrestrial once, always staying on the horizon, how far will it travel (in feet)?
Envelopes

Source:

3/15/2010
Tina writes four letters to her friends Silas, Jessica, Katie, and Lekan. She prepares an envelope for Silas, an envelope for Jessica, an envelope for Katie, and an envelope for Lekan. However, she puts each letter into a random envelope. What is the probability that no one receives the letter they are supposed to receive?
probability
SMT 2007 Algebra #8

Source:

6/27/2012
If r+s+t=3r+s+t=3, r2+s2+t2=1r^2+s^2+t^2=1, and r3+s3+t3=3r^3+s^3+t^3=3, compute rstrst.
LaTeX