MathDB

10

Part of 2007 Stanford Mathematics Tournament

Problems(3)

SMT 2007 Team #10

Source:

6/30/2012
A nondegenerate rhombus has side length ll, and its area is twice that of its inscribed circle. Find the radius of the inscribed circle.
geometryrhombus
Friends

Source:

3/15/2010
Al, Betty, and Clara are in the same class of 50 students total, but are not friends with each other. Al is friends with 24 students, Betty is friends with 39, and Clara is friends with 20. What is the greatest number of students that could be friends with all 3 of them?
SMT 2007 Algebra #10

Source:

6/27/2012
Evaluate ∑k=12007(−1)kk2\sum_{k=1}^{2007}(-1)^{k}k^{2}