MathDB

4

Part of 2009 Stanford Mathematics Tournament

Problems(3)

SMT 2009 Algebra 4

Source:

12/27/2011
Find all values of xx for which f(x)+xf(1x)=xf(x)+xf\left(\frac{1}{x}\right)=x for any function f(x)f(x)
function
SMT 2009 Geometry 4

Source:

12/27/2011
ABCDABCD forms a rhombus. EE is the intersection of ACAC and BDBD. FF lie on ADAD such that EFEF is perpendicular to FDFD. Given EF=2EF=2 and FD=1FD=1. Find the area of the rhombus ABCDABCD
geometryrhombus
SMT 2009 Team 4

Source:

12/27/2011
How many ways are there to write 657657 as a sum of powers of two where each power of two is used at most twice in the sum? For example, 256+256+128+16+1256+256+128+16+1 is a valid sum.