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Topic: cotpi 69 - Black and white plane
Replies: 26   Last Post: Oct 9, 2013 10:23 AM

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quasi

Posts: 10,450
Registered: 7/15/05
Re: cotpi 69 - Black and white plane
Posted: Oct 2, 2013 3:15 PM
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Pubkeybreaker wrote:
>Susam Pal wrote:
>>
>> How can you construct a plane where every point is coloured
>> either black or white such that two points of the same colour
>> are never a unit distance apart?
>>
>> -- Originally posted at:
>> http://cotpi.com/p/69/
>> Puzzles IRC channel:
>> ##puzzles on irc.freenode.net
>> Puzzles IRC webchat:
>> http://webchat.freenode.net/?channels=##puzzles

>
>It does not seem possible. Take any point. Suppose it is
>white. It is the center of a circle (of radius 1). All points
>on that circle must then be black. But given any point on
>that circle there is another point on the circle at distance 1.
>Both points are the same color.
>
>Unless, of course, I am being completely stupid.


No, your proof is fine.

quasi


Date Subject Author
10/2/13
Read cotpi 69 - Black and white plane
cotpi
10/2/13
Read Re: cotpi 69 - Black and white plane
Pubkeybreaker
10/2/13
Read Re: cotpi 69 - Black and white plane
quasi
10/2/13
Read Re: cotpi 69 - Black and white plane
Mike Terry
10/6/13
Read Re: cotpi 69 - Black and white plane
David Bernier
10/6/13
Read Re: cotpi 69 - Black and white plane
David Bernier
10/6/13
Read Re: cotpi 69 - Black and white plane
David Bernier
10/6/13
Read Re: cotpi 69 - Black and white plane
David Bernier
10/6/13
Read Re: cotpi 69 - Black and white plane
David Bernier
10/6/13
Read Re: cotpi 69 - Black and white plane
quasi
10/6/13
Read Re: cotpi 69 - Black and white plane
quasi
10/6/13
Read Re: cotpi 69 - Black and white plane
David Bernier
10/6/13
Read Re: cotpi 69 - Black and white plane
David Bernier
10/6/13
Read Re: cotpi 69 - Black and white plane
quasi
10/6/13
Read Re: cotpi 69 - Black and white plane
David Bernier
10/9/13
Read Re: cotpi 69 - Black and white plane
Phil Carmody
10/9/13
Read Re: cotpi 69 - Black and white plane
David Bernier
10/2/13
Read Re: cotpi 69 - Black and white plane
Eric Lafontaine
10/2/13
Read Re: cotpi 69 - Black and white plane
Michael F. Stemper
10/2/13
Read Re: cotpi 69 - Black and white plane
quasi
10/2/13
Read Re: cotpi 69 - Black and white plane
quasi
10/2/13
Read Re: cotpi 69 - Black and white plane
Haran Pilpel
10/2/13
Read Re: cotpi 69 - Black and white plane
quasi
10/2/13
Read Re: cotpi 69 - Black and white plane
quasi
10/2/13
Read Re: cotpi 69 - Black and white plane
Ted Schuerzinger
10/2/13
Read Re: cotpi 69 - Black and white plane
Mark Brader
10/3/13
Read Re: cotpi 69 - Black and white plane
William Elliot

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