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Topic: Algorithm for deriving permutations
Replies: 26   Last Post: Oct 21, 2007 2:16 PM

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mensanator

Posts: 5,039
Registered: 12/6/04
Re: Algorithm for deriving permutations
Posted: Oct 19, 2007 1:24 AM
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On Oct 18, 10:53?pm, Patrick Hamlyn <p...@multipro.N_OcomSP_AM.au>
wrote:
> Water Cooler v2 <wtr_...@yahoo.com> wrote:
>
>
>
>
>

> >If you have, say, 4 boxes to put the following 6 types of things in:
>
> >Apples
> >Oranges
> >Pears
> >Bananas
> >Gooseberry
> >Lemon

>
> >Such that you could:
>
> >a) only put one piece of each of the things in one box; and
>
> >b) you could put the same thing in all the boxes, i.e you could put,
> >say, an apple each in each of the boxes. In the mathematical jargon,
> >if repetition was allowed

>
> >Then, I know that we could have 6*6*6*6, i.e 1296 permutations.
>
> >However, I want to know the algorithm to decide what those
> >combinations are. Help appreciated.

>
> I've seen a bunch of algorithms posted, whether loops or recursions, but you
> don't need any of those.
>
> Simply represent each box by a digit in a number in base 6.
>
> Now each combination is numbered. If you want the 1000th combination, you can
> generate it directly by converting 1000 to base 6. The nth digit gives the nth
> bin's contents.


But that includes ALL combinations. Sounds more
like th OP wants the 1000th combination of just
the 4-digit base 6 numbers.

base10: 1000 base6: 4344
But...
base6: 4344 is the 785th 4-digit base 6 number
The 1000th 4-digit base 6 number...
...is 5343.

base10: 1100 base6: 5032
But...
base6: 5032 is the 885th 4-digit base 6 number
The 1100th 4-digit base 6 number...
...does not exist, there are only 1080 of them.


>
> The same works for 1000000 types of object in 1000000 bins. The arithemetic is
> more tedious and the numbers larger, but you can still produce the Xth
> combination directly without loops.
> --
> Patrick Hamlyn posting from Perth, Western Australia
> Windsurfing capital of the Southern Hemisphere
> Moderator: polyforms group (polyforms-subscr...@egroups.com)- Hide quoted text -
>
> - Show quoted text -






Date Subject Author
10/18/07
Read Algorithm for deriving permutations
Water Cooler v2
10/18/07
Read Re: Algorithm for deriving permutations
Randy Poe
10/18/07
Read Re: Algorithm for deriving permutations
Water Cooler v2
10/18/07
Read Re: Algorithm for deriving permutations
hardwidg
10/18/07
Read Re: Algorithm for deriving permutations
Richard Heathfield
10/18/07
Read Re: Algorithm for deriving permutations
Proginoskes
10/18/07
Read Re: Algorithm for deriving permutations
Robert Israel
10/18/07
Read Re: Algorithm for deriving permutations
Proginoskes
10/19/07
Read Re: Algorithm for deriving permutations
David Bernier
10/19/07
Read Re: Algorithm for deriving permutations
Richard Heathfield
10/21/07
Read Re: Algorithm for deriving permutations
Richard the Dreaded Libertarian
10/21/07
Read Re: Algorithm for deriving permutations
Richard the Dreaded Libertarian
10/18/07
Read Re: Algorithm for deriving permutations
Randy Poe
10/19/07
Read Re: Algorithm for deriving permutations
David Breton
10/19/07
Read Re: Algorithm for deriving permutations
Proginoskes
10/19/07
Read Re: Algorithm for deriving permutations
Richard Harter
10/19/07
Read Re: Algorithm for deriving permutations
Marshall
10/19/07
Read Re: Algorithm for deriving permutations
Patricia Shanahan
10/18/07
Read Re: Algorithm for deriving permutations
briggs@encompasserve.org
10/18/07
Read Re: Algorithm for deriving permutations
Patrick Hamlyn
10/19/07
Read Re: Algorithm for deriving permutations
mensanator
10/19/07
Read Re: Algorithm for deriving permutations
hagman
10/19/07
Read Re: Algorithm for deriving permutations
Patrick Hamlyn
10/19/07
Read Re: Algorithm for deriving permutations
Richard Heathfield
10/19/07
Read Re: Algorithm for deriving permutations
mensanator
10/19/07
Read Re: Algorithm for deriving permutations
rossum
10/20/07
Read Re: Algorithm for deriving permutations
Grouchy

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