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

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

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New post 03 Jun 2009, 01:11
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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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Re: Tough DS 9  [#permalink]

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New post 03 Jun 2009, 01:40
B shud be the answer..

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.
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Re: Tough DS 9  [#permalink]

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New post 03 Jun 2009, 23:33
hades ??

whats the answer ?
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Re: Tough DS 9  [#permalink]

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New post 04 Jun 2009, 00:03
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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Hades

Re: Tough DS 9 &nbs [#permalink] 04 Jun 2009, 00:03
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