Panex Puzzle:


This is a port of Panex puzzle for X Window.

The original Panex puzzle is from the Japanese Magic Company
from the 1980's. Mathematicians at Bell Laboratories estimated
the  number  of  moves  to  swap  2  columns of order 10 to be 
27,564 <= N <= 31,537. It  came  in two  varieties: one with a
blue and a yellow pyramid of order 10 on  silver tiles; in the
gold version pieces of each color  look  alike i.e. no pyramid
is drawn on them), this is a little harder.
The  original  Tower  of  Hanoi  puzzle is the  invention of
Edouard  Lucas  and  was sold as a toy in France in  1883. The
legend  of 64  disks in the great temple of Benares of the god 
Brahma is also his invention.


Mark Manasse, Danny Sleator & Victor K. Wei.  Some Results on the Panex Puzzle.  Preprint sent by Jerry Slocum, 23pp, nd [c1985].  For piles of size  n,  the minimum number of moves,  T(n),  to move one pile to the centre track is determined by means of a 2nd order, non-homogeneous recurrence which has different forms for odd and even  n.  Compensating for this leads to a 2nd order non-homogeneous recurrence, giving  T(10) = 4875  and  T(n) ~  C(1 + (2)n.  This solution doesn't ever move the other pile.  The minimum number of moves,  X(n),  to exchange the piles is bounded above and below and determined exactly for  n ( 7  by computer search.  X(6) = 881,  compared to the bounds of  796  and  881.  For  n = 10, the bounds are  27,564  and  31,537.

Quantum
Nesting Puzzles (part I: The Tower of Hanoi and Panex), 
Vladimir Dubrovsky, Jan/Feb96, p53 (Toy Store) 

Nesting Puzzles (part II: Chinese rings and the return of the dragon), 
Vladimir Dubrovsky, Mar/Apr96, p61 (Toy Store) 


- A. J. van Zanten, 
  An optimal algorithm for the twin-tower problem, 
  Delft Progress Report 15 (1991), 33-50. MR 92a:05001. 

- A. J. van Zanten, 
  An iterative optimal algorithm for the generalized tower of
  Hanoi problem, Internat. J. Comput. Math. 39 (1991), 163-168. 


- David Bagley; 
  Java Applet, 1-10 Layers, Solver, Info
  http://www.tux.org/~bagleyd/java/PanexApp.html
  Gets X(6) = 881.

- Java Applet (4 Layers)
  http://cheesygames.com/panex/