Alexander's Knight Puzzle

In the computer game The 7th Guest, one of the memorable puzzles was, given a 4x5 chessboard (as below), place four black bishops on ABCD and four white bishops on abcd, then using only valid chess moves, move all the black bishops to abcd and the white bishops to ABCD. At no time may any piece be under attack by the opposite color. You might enjoy trying to solve this puzzle - it's not too difficult with a little trial and error.
 4x5 board
+--+--+--+--+--+
| A| 1| 5| 9| a|
+--+--+--+--+--+
| B| 2| 6|10| b|
+--+--+--+--+--+
| C| 3| 7|11| c|
+--+--+--+--+--+
| D| 4| 8|12| d|
+--+--+--+--+--+ 
The puzzle I'm more interested in is this: Alexander Doskey suggests you repeat this puzzle, using knights. Moves do not need to alternate in color.

Source: Reader Alexander Doskey.


Solution
Mail to Ken