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 Forum index » Diversions » Perplex City Puzzle Cards » PXC: Orange Puzzle Cards
#039 - 4 Colour Theorem
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number9dream
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Joined: 22 Apr 2005
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Location: Newcastle, UK

 		#039 - 4 Colour Theorem
Guest puzzle architect Tom Boardman

Imagine you're a mapmaker.

One of the more enjoyable parts of your job is when you get to colour a brand new map. All sorts of wierd and wonderful map cross your desk and you have to decide how different areas are coloured, ensuring that no border segments share the same colour.

You only ever use four colours (red, green, blue and yellow), knowing that it would be impossible with 3 and a waste of ink to use 5.*

This imaginary country is divided into nineteen different regions. While it can be coloured in many different ways, all of them require the area marked ? to be one particular colour.

What colour must it be?
*Discovering why 4 colours is always sufficient managed to perplex mathematicians for decades.
4 colour theorem.jpg
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4 colour theorem.jpg
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Sometimes I think the surest sign that intelligent life exists elsewhere in the universe is that none of it has tried to contact us.

PostPosted: Sat Apr 08, 2006 7:04 am
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fretty
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Joined: 19 Nov 2004
Posts: 281
Location: South Yorkshire, England
Spoiler (Rollover to View):
The shape must be coloured in yellow


PostPosted: Sat Apr 08, 2006 7:22 am
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groovygirl20
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Joined: 04 Jan 2006
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Location: Lincolnshire! ENGLAND!! WOO!!

 		surely it could be any of them really because there are so many options for all the other shapes?!
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PostPosted: Thu Apr 20, 2006 10:28 am
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Mindez
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Joined: 26 Feb 2006
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 		Wrong. When colouring in all the ones that you are FORCED to colour in (Otherwise it won't work), you get:

Spoiler (Rollover to View):
http://www.tamino.co.uk/4colourtheorem.PNG


Every colour filled in on that picture HAS to be filled in like that, and cannot be replaced by another colour.

PostPosted: Thu Apr 20, 2006 11:00 am
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Carma1313
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Joined: 20 Apr 2006
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Location: Gravesend, Kent, England

 		Oops... I made the mistake of not colouring in the middle segment

PostPosted: Fri Apr 21, 2006 9:35 am
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groovygirl20
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Joined: 04 Jan 2006
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Location: Lincolnshire! ENGLAND!! WOO!!

 		meh... me 2 lol
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To the query, ''What is a friend?'' his reply was ''A single soul dwelling in two bodies.''

PostPosted: Fri Apr 21, 2006 3:09 pm
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