I am hiring someone for a job. My top two candidates are nearly identical. When I way the weaknesses and strengths of one candidate against the weaknesses and strengths of another, they are perfectly equal. There's a paradox here. If I am a philosopher and use reason and logic to answer problems, what do I do when all my analytic skills bring me to a point where it goes no further? Which candidate does a philosopher choose? Doesn't this show a limit of our own ability to reason?
A traditional version of this puzzle is referred to as 'Buridan's ass'. It postulates that a donkey put equidistant between two identical stacks of hay might starve out of inability to choose between them. If reason says that they are equally qualified for the position and either will do just fine, then any (morally acceptable) arbitrary criterion would do. So, I would simply flip a coin. I don't think the puzzle shows anything disturbing about the limits of reason. After all, you merely stipulated that the candidates were identically qualified.