How can you rearrange checkers pieces in 3 moves to separate white and black?

[lendav_rott]

I have a book called "Tricky math" or something along those lines (not in English) with interesting problems.

There are 6 checkers pieces, 3 white and 3 black.
You have a line with 10 slots numbered 1, 2, 3 .. 10.
The pieces are placed in slots 5, 6, 7, 8, 9, 10 such that 5 is white, 6 black, 7 white, 8 black, 9 white and 10 black.

We are to rearrange the pieces in 3 moves such that all the white pieces are on the left and all the black pieces on the right. We are allowed to only move 2 adjacent pieces at a time Without rearranging their order. Adjacent according to slot numbers, which means not allowed to move, say 6 and 9 if 7 and 8 were empty.

 

[verty]

Luckily this is not too tricky. Solutions to questions like this one usually have a symmetrical structure. This puzzle is no exception. The last two moves mirror each other.