All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Games
4x3 Knight Swap (Posted on 2010-04-05) Difficulty: 3 of 5
Six chess knights are placed on a 4x3 chessboard, three along the top row and three along the bottom, which are labeled as P, Q, R, X, Y, Z, as shown in the figure below.

Exchange the positions of P and X, Q and Y and, R and Z, in minimum possible number of moves.

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Thoughts | Comment 3 of 5 |

1. Take off all the pieces first.

2. Q to y is 3 moves*2 knights = 6

3. x to p is 5 moves*4 knights = 20

Therefore the minimum is 26.

Q and y can easily be made to translate without blocking (eg qa2, ya3; qb3, yc2; qb1, yb4.

So we can simply remove those squares from the board, if we can show that x can get from a1 to a4 without using them; e.g xc2,xa3,xc4,xb2,xc4 (not a unique solution) AND that this doesn't result in a roadblock during the translations requring a backward step:

 xc2 xa3 x's next move is blocked, so     
 rb2 xc4 r's next move is blocked, so     
 pc3 ra4 xb2 pa2 rc3 xa4!  
 p's next move is blocked, so       
 zb3 za1 zc2 za3 zc4!   
 Then pc1 pb3 pa1!   
 Then ra2 rc1! 

This requires 20 moves, so would seem to be a minimum solution, but no doubt there is a more analytical method.

  Posted by broll on 2010-04-06 05:13:45
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information