Combination Algorithm without brut force - Combine 4's into least 6's

*To*: mathgroup at smc.vnet.net*Subject*: [mg27284] Combination Algorithm without brut force - Combine 4's into least 6's*From*: "aufempenmss" <aufempen at modemss.brisnet.org.au>*Date*: Fri, 16 Feb 2001 03:58:43 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

I have Mathematica 2.2 for WIN3.1 and I have not got much combinatorial functions on it. Could you please help? May be I should post this on the Wolfram forum? which one? What is the algorithm or principle to combine all the combinations of 4s into the smallest combination of 6s from a range of 10 consecutive numbers? What is the combinatorix formula for the least combination of 6s? Here is the data 1) All the combinations of 4s in a range of 10 numbers 1 1 2 3 4 2 1 2 3 5 3 1 2 3 6 .... The full result of all combinations of 4s has been truncated to save space on this postingl ...... 208 6 7 9 10 209 6 8 9 10 210 7 8 9 10 2) The result for combining all 4s into the least number of 6s is 21 combinations of 6s: But how do you set the algorithm or explain how it works without using brut force? 1 1 2 3 4 5 6 2 1 2 3 4 7 8 3 1 2 3 4 9 10 4 1 2 4 5 7 10 5 1 2 4 6 8 9 6 1 2 5 6 7 9 7 1 2 5 6 8 10 8 1 3 5 6 7 8 9 1 3 5 6 9 10 10 1 3 7 8 9 10 11 1 4 5 8 9 10 12 1 4 6 7 9 10 13 2 3 4 5 8 10 14 2 3 4 6 7 9 15 2 3 5 7 9 10 16 2 3 6 8 9 10 17 2 4 5 7 8 9 18 2 4 6 7 8 10 19 3 4 5 6 7 10 20 3 4 5 6 8 9 21 5 6 7 8 9 10 Brut force = Obtaining these numbers by designing my computer program to number crunched all possibilities. 3)Any explanation, containing combination, permutation, group mathematics will be appreciated. Please post to aufempen at modemmss.brisnet.org.au