I'm sorry that I didn't make it clear that the problem was to keep the order of the knights, i.e., White knight Si is to swap places with Black knight si for i = 1, 2, ..., n. R. On Sun, 17 Oct 2010, Lior Manor wrote:

Hi, Maybe I got it wrong, but it seems that the following is an 8 steps solution for n=3:

s s s   s s S s s S s   S s   S s S S   S S S S S S S           s     s     s S   s     s     s     s       S S S S S S S   S S s S S s   S s   S s s   s s s s s

Am I missing something?

Lior

On Fri, Oct 15, 2010 at 21:53, Richard Guy <rkg@cpsc.ucalgary.ca> wrote: I don't believe that the following sequence is in OEIS.

The (least) number of moves needed to swap n  pairs of knights on a  3 by n  chessboard.

I.e., the number of chess knight moves needed to get from

S  S  S  ...  S          s  s  s  ...  s -  -  -       -    to    -  -  -       - s  s  s  ...  s          S  S  S       S

where  s,  S  are chess knights of opposite colors.  Not possible for  n = 1, 2, 3.

n = 4: 32 moves are necessary and sufficient.

n = 5, 6, 7, ... are Rikki-Tikki-Tavi questions on p.250 (R187) of The Inquisitive Problem Solver.

R.

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