What would have been our number system if humans had more than 10 fingers? Try to solve this puzzle. Try to solve this puzzle:

The first expedition to Mars found only the ruins of a civilization.
  From the artifacts and pictures, the explorers deduced that the
  creatures who produced this civilization were four-legged beings with
  a tentatcle that branched out at the end with a number of grasping
  "fingers". After much study, the explorers were able to translate
  Martian mathematics. They found the following equation:
  $$5x^2 - 50x + 125 = 0$$
  with the indicated solutions $x=5$ and $x=8$. The value $x=5$ seemed
  legitimate enough, but $x=8$ required some explanation. Then the explorers 
  reflected on the way in which Earth's number system developed, and found
  evidence that the Martian system had a similar history. How many fingers would 
  you say the Martians had?
$(a)\;10$
$(b)\;13$
$(c)\;40$
$(d)\;25$

P.S. This is not a home work. It's a question asked in an interview.

Yet another way to find it, using the unexploited piece of data that we are proposed with possible solutions to avoid any non trivial mental calculus.


*

*$x=8$ being a solution rules out solution (a), base = 10.

*As $x=5$ is a root wathever the base b used by martians we will have: $$5.5.5-5.5.b+b^2+5.b+5=0$$  From wich we trivially get: $$25 b - 125 > b^2$$
Obviously 25 is already too large, it rules out solution (c) and it also rules out 40, solution (d).
We are left with solution (b), martian have 13 digits, which we should still check as a valid answer.
Of course other answers are better as they do not rely on fixed list of proposed possible solutions.
