[Guest]

Eight 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.

3x4 chess.bmp

[superprismatic]

It can be done in a minimum of 32 moves. I'll post a sequence of such moves tomorrow as I have no time to do it now.

Edited January 16, 2010 by superprismatic

[superprismatic]

Here is a minimal sequence of moves that

satisfies the OP:

PQRS
---- START
TUVW

PQRS
-W-- 1
TUV-

PQ-S
-W-- 2
TUVR

PQUS
-W-- 3
T-VR

P-US
-W-Q 4
T-VR

P-US
-W-- 5
TQVR

P--S
UW-- 6
TQVR

P-QS
UW-- 7
T-VR

--QS
UW-- 8
TPVR

--QS
UW-P 9
T-VR

--QS
UWTP 10
--VR

-PQS
UWT- 11
--VR

--QS
UWT- 12
P-VR

-VQS
UWT- 13
P--R

-VQS
-WT- 14
P-UR

-V-S
-WT- 15
PQUR

---S
-WTV 16
PQUR

Q--S
-WTV 17
P-UR

QU-S
-WTV 18
P--R

QURS
-WTV 19
P---

QU-S
-WTV 20
PR--

QU--
-WTV 21
PRS-

QU-W
--TV 22
PRS-

QU-W
S-TV 23
PR--

QUSW
--TV 24
PR--

QU-W
--TV 25
PR-S

QURW
--TV 26
P--S

QU-W
R-TV 27
P--S

QU-W
--TV 28
P-RS

QU-W
--T- 29
PVRS

QUVW
--T- 30
P-RS

-UVW
--T- 31
PQRS

TUVW
---- 32
PQRS