TITLE: How many fingers do martians have?
QUESTION [10 upvotes]: Text of problem: It is supposed that we use base 10 as our number system because we have ten fingers.
A martian, after seeing the equation
$x^2-16x+41=0$
writes the difference of the roots as $10$.
End
How many fingers do martians have ?
Note: For numbers between $0$ and $6$, Martians' writing is the same as ours.
I have absolutely no idea how to solve that.

REPLY [16 votes]: Note that the sum of the roots is $A+B=16$ from the quadratic, and the difference is $A-B=10$. Add these to obtain $2A=26$ or $A=13$ and then $B=3$ all in martian. So in martian also $3\times 13=41$ and it is easy from there.