Re^2: Best possible counts for a few test cases (in readmore) (Hanoi Challenge)


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Re^2: Best possible counts for a few test cases (in readmore) (Hanoi Challenge)

by tye (Sage)

on Oct 22, 2004 at 20:18 UTC ( [id://401670]=note: print w/replies, xml )

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in reply to Re: Hanoi Challenge
in thread Hanoi Challenge

It can be done more efficiently than this. You shouldn't divide the work up evenly. Below are some special cases and the smallest solution sizes possible (I believe) for them.

If P is the number of pegs, D is the number of disks, and M is the minimum number of moves for which a solution exists, then:

for  P >= 3
if   D = P*(P-1)/2
then M = P*(P-2)*2+1

so

P=3, D=3,  M=7
P=4, D=6,  M=17
P=5, D=10, M=31
P=6, D=15, M=49
...
[download]

So I can beat your 35-move solution for the 5P10D case by 4 moves.

I may write up why this is so, but I suspect someone else is likely to beat me to that. And if you try to figure out why I picked these cases, you'll probably have a good hint for part of a good solution for the general problem. (:

- tye