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Following are the four regions 1, 2, 3 and 4 and they need to be color

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Intern
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Following are the four regions 1, 2, 3 and 4 and they need to be color [#permalink]

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New post 08 Mar 2011, 18:22
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E

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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.
Image

A. 4
B. 6
C. 9
D. 24
E. 36



[Reveal] Spoiler:
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[Reveal] Spoiler: OA

Last edited by Bunuel on 16 May 2017, 08:00, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Director
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Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
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Re: Following are the four regions 1, 2, 3 and 4 and they need to be color [#permalink]

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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: Following are the four regions 1, 2, 3 and 4 and they need to be color [#permalink]

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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
Director
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Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 899
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Re: Following are the four regions 1, 2, 3 and 4 and they need to be color [#permalink]

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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.
Re: Following are the four regions 1, 2, 3 and 4 and they need to be color   [#permalink] 08 Mar 2011, 19:29
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Following are the four regions 1, 2, 3 and 4 and they need to be color

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