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4

Part of 2001 Putnam

Problems(2)

Putnam 2001 A4

Source:

2/26/2012
Triangle ABCABC has area 11. Points EE, FF, and GG lie, respectively, on sides BCBC, CACA, and ABAB such that AEAE bisects BFBF at point RR, BFBF bisects CGCG at point SS, and CGCG bisects AEAE at point TT. Find the area of the triangle RSTRST.
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Putnam 2001 B4

Source:

2/27/2012
Let SS denote the set of rational numbers different from {−1,0,1} \{ -1, 0, 1 \} . Define f:S→Sf: S \rightarrow S by f(x)=x−1/xf(x)=x-1/x. Prove or disprove that ∩n=1∞f(n)(S)=∅ \cap_{n=1}^{\infty} f^{(n)} (S) = \emptyset where f(n)f^{(n)} denotes ff composed with itself nn times.
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