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

*To*: mathgroup at smc.vnet.net*Subject*: [mg27287] [mg27287] Re: [mg27284] Combination Algorithm without brut force - Combine 4's into least 6's*From*: BobHanlon at aol.com*Date*: Sun, 18 Feb 2001 02:52:19 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Needs["DiscreteMath`Combinatorica`"]; Use KSubsets Length[KSubsets[Range[10], 4]] == Binomial[10, 4] == 210 True I have no idea of what you mean by "combining all 4s into the least number of 6s" Bob Hanlon In a message dated 2001/2/16 4:43:29 AM, aufempen at modemss.brisnet.org.au writes: >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 >