Three knights on a 3x3 chess board

There are two white knights (W) and black nights(B) positioned at a 3x3 chess board. Find them minimum number of moves required to replace the black knights with the whites.Any type of move is allowed not necessarily alternating black and white.No capturing is allowed white or black knights can not move to block which is already filled with any other knight(black or white). The position at which the whites knights were before is to be replaced by the black knights similarly white knights are to be placed where black knights were initially .I tried to do this but not able to finally find a answer. I am confused.

• You can do it in sixteen moves, just let them move around in a circle! I would even say that this is the minimum number of moves (if it is not allowed for two knights to occupy the same field at the same time). – Zardo Jul 19 '15 at 11:36
• @Achal: Can u tell , if the rules are the same as standard chess, example if the white knight is in the capturing zone of black knight then can black knight capture the white knight ? – R K Jul 19 '15 at 11:41
• I have to ask the same as @RK. And I would like further clarification. Are you able to move any piece, black or white, or do they have to be moved in the usual chess pattern of turns? If turns are not followed, and one may replace the black knights, then just move the white knights to the middle, then replace the black knights with them. That is 4 moves and is the absolute minimum you can have. – zagadka314 Jul 19 '15 at 11:51
• Please elaborate. What sort of moves are allowed? Alternating black and white, or any moves? Captures? What do you mean by "replace"? Should they swap places, or is the black knight "replaced" by a white knight as soon as the white knight takes its place? – joriki Jul 19 '15 at 12:06
• An observation that might be of use: the middle square is redundant. It can never be reached. – Colm Bhandal Jul 19 '15 at 16:26

1 Answer

HINT: ‘Untwist’ the board by converting this:

$$\begin{array}{|c|c|c|} \hline \color{blue}0&3&\color{brown}6\\ \hline 5&&1\\ \hline \color{blue}2&7&\color{brown}4\\ \hline \end{array}$$

to this:

$$\begin{array}{|c|c|c|} \hline \color{blue}0&1&\color{blue}2\\ \hline 7&&3\\ \hline \color{brown}6&5&\color{brown}4\\ \hline \end{array}$$