There is just one way to go from XXXXOOOO to XOXOXOXO in five moves if *three* adjacent coins are moved at each turn. How?

I can't figure out a definition tha limits the solutions to one :-( And these assume that I don't move more than three coins away from the original set. And I found 6 translate solutions for the reverse pattern of OXOXOXOX.

 

Looks like nikki's symmetry statement is kicking in.

And yeah nikki, I too, finally decided that gaps in the final answer are not good under your translate definition. But I still think the rotaters are cool, but I shall abstain :-)

 

_,_,_,X,X,X,X,O,O,O,O,_,_,_

_,_,_,X,X,_,_,_,O,O,O,X,X,O

_,_,_,X,X,O,O,O,_,_,_,X,X,O

_,_,_,X,_,_,_,O,X,O,O,X,X,O

_,_,_,X,O,X,X,O,X,O,_,_,_,O

_,_,_,_,_,_,X,O,X,O,X,O,X,O

 

_,_,_,X,X,X,X,O,O,O,O,_,_,_

X,O,O,X,X,X,_,_,_,O,O,_,_,_

X,O,O,_,_,_,X,X,X,O,O,_,_,_

X,O,O,X,X,O,X,_,_,_,O,_,_,_

X,_,_,_,X,O,X,O,O,X,O,_,_,_

X,O,X,O,X,O,X,O,_,_,_,_,_,_

Edited on October 27, 2004, 11:38 pm

Posted by owl on 2004-10-27 23:33:48