I wouldn’t apply for the reward with that answer.
You know, mathematicians are weird breed. When they could not solve some equations with integers, they invented the fractions, when that didn’t work they invented “real” numbers with sign “-” in front, when that didn’t work, they imagined the complex numbers. And when that didn’t work they started inventing multiple (over 3) dimensions to make the number of equations equal the number of unknowns.
I think there is a solution but someone has to imagine or invent something else that doesn’t yet exist.