30 segments of lengths 1, \sqrt3, \sqrt5, \sqrt7, ..., \sqrt{59}
Source: Argentina 1994 OMA L3 p1
May 13, 2024
combinatoricscombinatorial geometry
Problem Statement
segments of lengths1, \sqrt{3}, \sqrt{5}, \sqrt{7}, \sqrt{9}, \ldots , \sqrt{59} have been drawn on a blackboard. In each step, two of the segments are deleted and a new segment of length equal to the hypotenuse of the right triangle with legs equal to the two deleted segments is drawn.
After steps only one segment remains. Find the possible values of its length.