In partial answer to the second question, see the top of p.878 in Vol.4 of the 2nd edition of Winning Ways. I believe that this is also discussed in a recent book by Robert Hearne & Erik Demaine, but three copies of this have succesively disappeared from my possession. R. On Thu, 20 Jan 2011, Neil Bickford wrote:
If you happen to have a 15 puzzle lying around with a removable piece, you can make a harder puzzle by bandaging the pieces as follows: + - - - - + | A A E b | | F c E E | | F D g | | D h i | + - - - - +
Puzzle: Move AA from the upper-left corner to lower-right. If a move is counted as moving 1 piece any direction (including L-shaped paths)any number of squares, 131 moves are minimum.
Second puzzle: Is this the hardest 4x4 Sliding Block Puzzle there is? --Neil Bickford
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