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Isosceles triangle inscribed in red-blue-green circle


Best Answer plasmid, 05 July 2013 - 04:35 AM

Spoiler for counterexample
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9 replies to this topic

#1 witzar

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Posted 04 July 2013 - 12:57 PM

Each point of the circle is painted either red, blue or green.

Prove, that there exists isosceles triangle inscribed in the circle with all its vertices of the same color.


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#2 Yoruichi-san

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Posted 05 July 2013 - 03:47 AM

Spoiler for The simple solution for 3 colors...

 

Spoiler for There is probably a more elegant way of putting it, but...

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#3 witzar

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Posted 05 July 2013 - 04:26 AM

Spoiler for The simple solution for 3 colors...

Spoiler for


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#4 plasmid

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Posted 05 July 2013 - 04:35 AM   Best Answer

Spoiler for counterexample

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#5 Yoruichi-san

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Posted 05 July 2013 - 05:05 AM

Shoot, forgot about non-adjacent groupings :rolleyes:.  

 

Time for bed...got up way too early this morning...I'll leave it to plasmid ;).


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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page! Episode 3 is finally here!

When life hands me lemons, I make invisible ink.

#6 TimeSpaceLightForce

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Posted 06 July 2013 - 01:54 PM

ferriswheel.JPG

templates for paint-a-point

 


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#7 TimeSpaceLightForce

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Posted 06 July 2013 - 02:20 PM

Spoiler for


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#8 witzar

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Posted 06 July 2013 - 03:56 PM

Spoiler for plasmid was right

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#9 bonanova

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Posted 06 July 2013 - 08:04 PM

Spoiler for plasmid was right


Nice puzzle. I figured the number of points should be odd, to make other points become candidate pairs once a vertex was chosen. I was able to confirm 9 points were not enough. I fell asleep exploring 11.

Nice solve as well!
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#10 TimeSpaceLightForce

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Posted 06 July 2013 - 11:00 PM

 

Spoiler for plasmid was right


Nice puzzle. I figured the number of points should be odd, to make other points become candidate pairs once a vertex was chosen. I was able to confirm 9 points were not enough. I fell asleep exploring 11.

Nice solve as well!

 

Spoiler for


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