Problem #PRU-66394

Problems Algebra

Problem

All the positive fractions smaller than \(1\) with denominators not more than \(100\) are written in a row. Isley and Ella put signs \("+"\) or \("-"\) in front of any fraction, which does not yet have a sign before it. They write signs in turns, but it is known that Isley has to make the last move and calculate the resulting sum. If the total sum turns out to be an integer number, then Ella will give her a chocolate bar. Will Isley be able to get a chocolate bar regardless of Ella’s actions?