Sources page biographical material

5.A.4. PANEX PUZZLE
Invented by Toshio Akanuma (??SP). Manufactured by Tricks Co., Japan, in 1983. Described in Hordern, pp. 144-145 & 220, E35, and in S&B, p. 135. This looks like a Tower of Hanoi (cf 7.M.2) with two differently coloured piles of 10 pieces on the outside two tracks of three tracks of height 12 joined like a letter E. This is made as a sliding block puzzle, but with blockages -- a piece cannot slide down a track further than its original position.
Mark Manasse, Danny Sleator & Victor K. Wei. Some Results on the Panex Puzzle. Preprint sent by Jerry Slocum, 23pp, nd [1983, but S&B gives 1985]. 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  6 by computer search. X(5) = 343, compared to bounds of 320 and 343. X(6) = 881, compared to the bounds of 796 and 881. For n = 7, the bounds are 1944 and 2189, For n = 10, the bounds are 27,564 and 31,537. The larger bounds are considered as probably correct.

Christoph Hausammann. US Patent 5,261,668 -- Logic Game. Filed: 6 Aug 1992; patented: 16 Nov 1993. 1p abstract + 2pp text + 3pp diagrams. Essentially identical to Panex.

Vladimir Dubrovsky. Nesting Puzzles -- Part I: Moving oriental towers. Quantum 6:3 (Jan/Feb 1996) 53-59 & 49-51. Says Panex was produced by the Japanese Magic Company in the early 1980s. Discusses it and cites S&B for the bounds given above. Sketches a number of standard configurations and problems, leading to "Problem 9. Write out a complete solution to the Panex puzzle." He says his method is about 1700 moves longer than the upper bound given above.

Nick Baxter. Recent results for the Panex Puzzle. 4pp handout at G4G5, 2002. Describes the puzzle and its history. David Bagley wrote a program to implement the Manasse, Sleator & Wei methods. On 7 Feb 2002, this confirmed the conjecture that X(7) = 2189. On 26 Mar 2002, it obtained X(8) = 5359, compared to bounds of 4716 and 5359. It is estimated that the cases n = 9 and 10 will take 10 and 1200 years! If Moore's Law on the increase of computing power continues for another 20 years, the latter answer may be available by then. He gives a simplified version of the algorithm for the upper bound, which gets 31,544 for n = 10. He has a Panex page: www.baxterweb.com/puzzles/panex/ and will be publishing an edited and annotated version of the Manasse, Sleator & Wei paper on it.