This version of the puzzle: some of the better ones are listed in M. There is a considerable quantity of other programs on the Web which implement No disc may be placed on top of a smaller one.įor an illustration, run the HanoiVar demonstration program.Only one disc shall be moved at a time. In the minimum time (number of moves) using m = 3 pins :. Of size, and the Classic problem is to transfer all n discs Initially the stack is placed on the left-most pin in decreasing order Pins, and a stack of n perforated discs of graduated diameters. It comprises a base plate on which is mounted a row of m vertical Sporadically been sold as a children's puzzle under the name Tower of Bramah. Mathematician Lucas, in a paper published in 1883.Įquipped since with an entirely bogus "ancient oriental" provenance, it has If n mod 2 = 1 then 4*3^((n-1)/2) - 2 else 2*3^(n/2) - 2 fi end Īccording to Rouse Ball, the original puzzle was invented by the French Mention bases uncoloured in demo, apart from Classic_P ? Mention Stockmeyer's 4-pin Cyclic, Adjacent puzzles. Turtle: optimality proof m = 2 smallest-disc recursion ? See HanoiVar.txtĪntwerp: Case n = 1 in pseudocode? Generalise to m stacks on m pins?ĭomino: consider DBF,DAF,EAB,EAD(n) ?Īrbitrary initial/final configs. Rainbow: no recursions D(n) for DDD(n) etc? 11 -> complete 18 functions ? Tower of Hanoi Variations (HanoiVar 16), W.F.Lunnon Comments, Corrections and Modifications (01/09/05) (31/05/06) (24/08/07) (04/06/08) (05/06/10) (29/08/10) 24/09/10Ĭolours of discs are specified: if changed in HanoiVar, must reconcile !!ĭefine suboptimal solution as asymptotically same order of time as optimal.
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