Twelve Knights

Cut out the 4 corner squares of a standard 8 X 8 chessboard. Place 12 Knights on this modified chessboard, so that every position is under attack.

Source: Sudipta Das.

Solutions were received from Lou Cairoli, Algirdas Rascius, Graeme McRae, Jozef Hanenberg, David Peck, Philippe Fondanaiche.

Jozef Hanenberg simplified the problem by noting: "... a knight on a white field attacks only black fields and vice versa. So let's try to place six knights on the white fields that attack all (30) black fields. A solution is d3, f3, b5, f5, c6 and d7." [The only other pattern which achieves this is to move c6 to b7. Both are shown below. - KD] 
 ......
....K...
.....K..
..K...K.
........
..K.K...
........
 ......

 ......
....K.K.
........
..K...K.
........
..K.K...
........
 ......
I made the diagram to the right to try to identify black squares as 'o'. You can see that every 'o' is attacked by at least one knight 'K'. 
 .o.o.o
.o.oKoKo
o.o.o.o.
.oKo.oKo
o.o.o.o.
.oKoKo.o
o.o.o.o.
 o.o.o.
Once you have all the squares of one color attacked by six knights, you need merely invert the solution and merge to get twelve knights which attack all squares. Algirdas Rascius sent the three possible solutions: 
 ......
...KK...
..K..K..
.KK..KK.
........
..KKKK..
........
 ......

 ......
...KK.K.
..K.....
.KK..KK.
........
..KKKK..
........
 ......

 ......
.K.KK.K.
........
.KK..KK.
........
..KKKK..
........
 ......

Mail to Ken