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Re: Combination Algorithm without brut force - Combine 4's into least 6's
*To*: mathgroup at smc.vnet.net
*Subject*: [mg27287] Re: [mg27284] Combination Algorithm without brut force - Combine 4's into least 6's
*From*: BobHanlon at aol.com
*Date*: Sat, 17 Feb 2001 03:31:06 -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
>
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