[6548] in s-news-athena
COMBO OPTIMISATION BY ELIMINATING SUB SETS
daemon@ATHENA.MIT.EDU (News Reader)
Wed Mar 1 21:53:42 1995
To: s-news@utstat.toronto.edu
From: dwh@bom.gov.au (News Reader)
Date: Thu, 2 Mar 1995 01:16:55 GMT
COMBO OPTIMISATION BY ELIMINATING
DUPLICATE COMBO 4 & 5 SUB-SETS
Consider a simple example 7 number combination of 1,2,3,4,5,6,7
Represented as 6 number combination subsets.
6 from 7 standard combos as follows
combo 1 1, 2, 3, 4, 5, 6
combo 2 1, 2, 3, 4, 5, 7
combo 3 1, 2, 3, 4, 6, 7
combo 4 1, 2, 3, 5, 6, 7
combo 5 1, 2, 4, 5, 6, 7
combo 6 1, 3, 4, 5, 6, 7
combo 7 2, 3, 4, 5, 6, 7
All combinations have at most 5 numbers in common
Thus if I wanted to aviod combinations with 4 or 5 numbers
in common I could eliminate 6 out of the 7 combos.
Is there a general formula that can be applied
ie; to give minimum overlap of numbers for a given combination.
As seen in the 7 number combo set when broken into 6
number combo sub sets, each number appears in all but 1 combo
I'm sure there must be a formula ! You probably already know it ?
RULES
Thus for a combo of 7 numbers broken into 6 number sub sets
and eliminating all sub sets that share 4 or 5 numbers with any
other subset I am left with only 1 sub set.
If I had 8 numbers broken into 6 number sub sets, how many
6 number subsets would I have left is I applied the same rules.
ie; eliminating all combos which shared 4 or 5 numbers with
any other subset ?
If I had 9 numbers broken into 6 number sub sets ?
If I had 10 numbers broken into 6 number sub sets ?
etc........
There must be a general formula one can apply ?
Any help appreciated
Thanks
David
