IMO 2010 Shortlist A3

Let x1,...,x100 be nonnegative real numbers such that xi xi 1 xi 2 ¨ 1 for all i 1,...,100 (we put x101 x1, x102 x2)....

imomathematicsolympiadshortlistalgebra

IMO 2010 Shortlist A3

Category: Algebra

Problem

Let x1,...,x100 be nonnegative real numbers such that xi xi 1 xi 2 ¨ 1 for all i 1,...,100 (we put x101 x1, x102 x2). Find the maximal possible value of the sum S  100 ¸ i1 xixi 2. (Russia) Answer. .