  Using non-linear difference equations, combined with symbolic computations,
we make a detailed study of the running times of numerous variants of the
celebrated Quicksort algorithms, where we consider the variants of single-pivot
and multi-pivot Quicksort algorithms as discrete probability problems. With
non-linear difference equations, recurrence relations and experimental
mathematics techniques, explicit expressions for expectations, variances and
even higher moments of their numbers of comparisons and swaps can be obtained.
For some variants, Monte Carlo experiments are performed, the numerical results
are demonstrated and the scaled limiting distribution is also discussed.
