In order to overlap any previous numbers you have to swap with it atleast once. Now for every number at pos p you have atleast n-p-1 numbers to be swapped with. So solution will be >! $$\sum_{i=1}^n i = \frac{n*(n-1)}{2}$$ Example for 5 4 3 2 1 >! 5 needs to be swapped with 4 numbers >! 4 needs to be swapped with 3 numbers >! 3 needs to be swapped with 2 numbers >! 2 needs to be swapped with 1 number. >! >! Thus 1+2+3+4 = 10