I have a doubt about if the minimum amount of letters (or maps) to cover a sphere is 2 or 6. My answer is 2 but I'm not sure. I gave the following parametrizations:
$$\rho_{1}:(0,2\pi)\times(0,\pi)\to S ~\textrm{such that}~ \rho_{1}(u,v)=(\cos{u}\sin{v},\sin{u}\sin{v},\cos{v})$$ and $$\rho_{2}:(-\pi,\pi)\times(0,\pi)\to S ~\textrm{such that}~ \rho_{2}(u,v)=(\cos{u}\sin{v},\cos{v},\sin{u}\sin{v})$$ Obviously $\rho_{1}$ covers all the sphere except the half of circumference over the plane $xOz$ for $x\geq 0$ and $\rho_{2}$ covers all the sphere except the half of circumference over the plane $xOy$ for $x\leq 0$. That's why I say that the answer is two.
However in the notes of a professor I saw that he put a case analogous for an ellipsoid and said that it was 6.