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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