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Regions and Colors

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Regions and Colors [#permalink] New post 08 Mar 2011, 18:22
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Following are the four regions 1,2,3 and 4 and they need to be colored with 3 different colors but no two adjacent regions can have same color. For example, region 1 3 and 4 can be colored with same color and region 2 with a different color. How many such color combination exist with which the region can be colored.
[img]untitled.JPG[/img]

a) 4
b) 6
c) 9
d) 24
e) 36
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Re: Regions and Colors [#permalink] New post 08 Mar 2011, 18:26
1234
I can choose 4C3 colors and these three colors can be ordered in 3! ways. So 4! combination. The answer has to be more than 4!. Hence I will guess E.
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Re: Regions and Colors [#permalink] New post 08 Mar 2011, 18:50
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You have:

3 choices for the color of region 1
2 choices for the color of region 2 (must be different from region 1)
2 choices for the color of region 3 (must be different from region 2)
2 choices for the color of region 4 (must be different from region 2)

Multiplying your choices gives 3*2*2*2 = 24 colorings in total.
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Director
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Re: Regions and Colors [#permalink] New post 08 Mar 2011, 19:29
thanks Ian - yes I misinterpreted. This question is resisting any straight formulas or formal approach.

IanStewart wrote:
You have:

3 choices for the color of region 1
2 choices for the color of region 2 (must be different from region 1)
2 choices for the color of region 3 (must be different from region 2)
2 choices for the color of region 4 (must be different from region 2)

Multiplying your choices gives 3*2*2*2 = 24 colorings in total.
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Re: Regions and Colors [#permalink] New post 08 Mar 2011, 21:58
The answer is 24 (choice D).
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Re: Regions and Colors   [#permalink] 08 Mar 2011, 21:58
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