Hi ,
Suppose that you pick N numbers . What is the minimum number of "k-combinations" needed to cover all "m-combinations." ( m < k < N )
What is the formula to find out this ?
Example
We picked up 5 numbers from 1 to 5 . And we want to list enough 3-combinations to cover all 2-combinations.
2-combinations are C(5,2) = 10
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1-2
1-3
1-4
1-5
2-3
2-4
2-5
3-4
3-5
4-5
3-Combinations are C(5,3) = 10
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1-2-3
1-2-4
1-2-5
1-3-4
1-3-5
1-4-5
2-3-4
2-3-5
2-4-5
3-4-5
Minumum Number of 3-combinations needed to cover all 2-combinations is 4.
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1-2-3 ( Covers 1-2,1-3,2-3)
1-4-5 ( Covers 1-4,1-5,4-5)
2-4-5 ( covers 2-4,2-5 and also 4-5)
3-4-5 ( Covers 3-4,3-5 and also 4-5)