This is is not explored further, though its consequences can be seen on the 'Animate' pageĪ. 'off' the base disc is not necessarily the partition used to move 'on' the destination disc. The Frame-Stewart solution acknowledges that there are (generally) a number of partitions that are minimal thus the partition used for moving To achieve it is probably more interesting to most people.Ī hint when checking references/links is to verify whether the document is addressing 'the solution' or commenting on 'the presumed solution'.īecause of the looseness of definitions and assumptions, a useful link which ties things down is The problem as stated is to find the number of moves, though the algorithm used
Note that the original paper uses 'washers' for what we denote as 'discs'. This missing lemma, ie that the assumption generates an optimal solution, was noted by the journal editor and has not been proved since - hence the 'presumed' bit. Is obtainable by moving the top n k discs to a new disc (for a suitable value of n k) then optimally moving the remaining discs to the destination peg and moving The solutions depend on the assumption that an optimal solution It addresses broadly equivalent solutions by Frame and Stewart. The 'presumed optimal' solution was given in a paperīack in 1941 addressing the problem posed in 1939. Than our favourite value of p, which is 5. The particular case where p = 4 is called the Reve's puzzle, but is no more special The generalised Towers of Hanoi problem concerns moving multiple discs using p ≥ 3 pegs. This is currently predicted to be early in 2038.
When the animation is complete, the epoch of the internet will end. Here, Urban Legend has it that a number of WebMonks are watching (in shifts) theĪnimation you can see on the 'Animate' tab but with 32 discs on 3 pegs going really, really fast. However, of more relevance to the current generation is the e-Towers of Hanoi legend. Legend has it that a bunch of monks are moving a physical tower of 64 discs from one of three pegs to another when they finish, the world will end. The basic Towers of Hanoi problem is moving multiple discs on three pegs - there are more than enough discussions about this (eg see ).
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