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In a certain laboratory, chemicals are identified by a

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In a certain laboratory, chemicals are identified by a [#permalink] New post 30 Oct 2006, 03:33
In a certain laboratory, chemicals are identified by a color-coding system. There are 20 different chemicals. Each one is coded with either a single color or a unique two-color pair. If the order of colors in the pairs doesn't matter, what is the minimum number of different colors needed to code all 20 chemicals with either a single color or a unique pair of colors?

5
6
7
20
40
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 [#permalink] New post 30 Oct 2006, 05:15
My answer is 6.

For a label wiht only 1 color: 6
For a label with 2 colors: 6!/ 2!(6-2)! = 15

15+6 =21

But you can also work this out even without the mathematical computation and just counting out the possible labels.
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 [#permalink] New post 30 Oct 2006, 12:12
I agree ...6 is my answer too!
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 [#permalink] New post 30 Oct 2006, 23:27
Hermione wrote:
My answer is 6.

For a label wiht only 1 color: 6
For a label with 2 colors: 6!/ 2!(6-2)! = 15

15+6 =21

But you can also work this out even without the mathematical computation and just counting out the possible labels.

Good job! agree B it is
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  [#permalink] 30 Oct 2006, 23:27
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