Eight white chess knights are placed on a 3x4 chessboard, four along the top row and four along the bottom, which are labeled as P, Q, R, S, T, U, V and W, as shown in the figure.

Exchange the positions of P and T, Q and U, R and V, and S and W in minimum possible number of moves.

P	Q	R	S
T	U	V	W

Let the squares be identified from 1 through 12 being read from left to right down.

The exchange can be done in at least 32 moves.

       1      2      3      4
PQRS   PQRS   PQRS   PQ.S   PQUS
....   ..T.   .WT.   .WT.   .WT.
TUVW   .UVW   .UV.   .UVR   ..VR

5      6      7      8      9
PQ.S   P..S   P..S   P.QS   ..QS
UWT.   UWTQ   UWT.   UWT.   UWT.
..VR   ..VR   .QVR   ..VR   .PVR

10     11     12     13     14
..QS   .PQS   ..QS   .VQS   ..QS
UWTP   UWT.   UWT.   UWT.   UWTV
..VR   ..VR   P.VR   P..R   P..R

15     16     17     18     19
..QS   .UQS   .U.S   QU.S   QURS
.WTV   .WTV   .WTV   .WTV   .WTV
P.UR   P..R   PQ.R   P..R   P...

20     21     22     23     24
QU.S   QU..   QU..   QUS.   QU..
.WTV   .WTV   SWTV   .WTV   .WTV
PR..   PRS.   PR..   PR..   PR.S

25     26     27     28     29
QUR.   QU..   QU..   QU..   QUV.
.WTV   RWTV   .WTV   .WT.   .WT.
P..S   P..S   P.RS   PVRS   P.RS

30     31     32
.UV.   .UVW   TUVW
.WT.   ..T.   ....
PQRS   PQRS   PQRS

Edited on February 17, 2010, 6:31 am

Posted by Dej Mar on 2010-02-15 10:33:30