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.
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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