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# An N -sided polygon is to have each edge coloured so that no

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Manager
Joined: 13 May 2009
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An N -sided polygon is to have each edge coloured so that no [#permalink]

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03 Jun 2009, 00:11
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An $$N$$-sided polygon is to have each edge coloured so that no two adjacent sides share the same colour. If $$X$$ represents the minimum number of colours required, is $$X < 3$$?

(1) $$N < 6$$

(2) $$N^{3} + N^{2} + N$$ is odd.
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Senior Manager
Joined: 15 Jan 2008
Posts: 275

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03 Jun 2009, 00:40

1, insuffieint.. for n = 5, teh minimum colors needed are 3 and for n =4, the minimum colors need is 2.

2, equation shows n must be odd..
for n = 3, the minimum colors need is 3,
n=5, minimum colors need is 3,
n =7, nimum colors needed is 3.. so..on..

Hence B is sufficent to say that X is not less than 3.
Senior Manager
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03 Jun 2009, 22:33

Manager
Joined: 13 May 2009
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03 Jun 2009, 23:03
Final Answer, $$B$$.

(1) is INSUFFICIENT as the polygron can be a triangle/square/pentagon. if it's a square we just need 2 colours, but if it's an odd-shaped polygon, we'll always need 3...
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Re: Tough DS 9   [#permalink] 03 Jun 2009, 23:03
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