$100$ fractions are written on a board
Source: All-Russian 2007
May 4, 2007
number theory unsolvednumber theory
Problem Statement
fractions are written on a board, their numerators are numbers from to (each once) and denominators are also numbers from to (also each once). It appears that the sum of these fractions equals to for some odd . Prove that it is possible to interchange numerators of two fractions so that sum becomes a fraction with odd denominator.
N. Agakhanov, I. Bogdanov