Best Answer Yoruichi-san, 02 July 2013 - 07:23 AM

Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-) |

Guest Message by DevFuse

Started by witzar, Jun 29 2013 03:17 PM

Best Answer Yoruichi-san, 02 July 2013 - 07:23 AM

Spoiler for Okay, the *doh* solution...

Go to the full post
9 replies to this topic

Posted 29 June 2013 - 03:17 PM

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

Prove, that there exists segment of length 1 with both ends of the same color.

Posted 01 July 2013 - 04:53 PM

Spoiler for

Posted 01 July 2013 - 05:42 PM

Spoiler for

Spoiler for

Posted 01 July 2013 - 07:58 PM

Spoiler for points w/ paints

Posted 02 July 2013 - 02:09 AM

This is not true.

Spoiler for points w/ paints

Posted 02 July 2013 - 02:48 AM

Spoiler for Proof by contradiction

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

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

When life hands me lemons, I make invisible ink.

Posted 02 July 2013 - 07:23 AM Best Answer

Spoiler for Okay, the *doh* solution...

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

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

When life hands me lemons, I make invisible ink.

Posted 03 July 2013 - 08:36 AM

This is not true.Spoiler for points w/ paints

Spoiler for

Posted 03 July 2013 - 01:28 PM

This is not true.Spoiler for points w/ paints

Spoiler for

Pick a random real number from interval [0,100]. What is the probability that picked number is not 7? Clearly 100%. Does it follow, that picking 7 is impossible or that number 7 does not exists? Clearly not.

Divide unit circle into 6 equal arcs. Paint those arc blue and green alternately (so that six end points of the arcs are painted alternately too).

You have an "impossible" blue-green circle.

In fact you can take just one arc (1/6 of circle) and paint it any way you want. Then for each point P of the arc take a regular hexagon H inscribed in the unit circle such that P is a vertex of H, and paint the other 5 vertices of H alternately (regarding color of P). Again you have an impossible blue-green circle.

Posted 03 July 2013 - 05:06 PM

This is not true.Spoiler for points w/ paints

Spoiler forPick a random real number from interval [0,100]. What is the probability that picked number is not 7? Clearly 100%. Does it follow, that picking 7 is impossible or that number 7 does not exists? Clearly not.

Divide unit circle into 6 equal arcs. Paint those arc blue and green alternately (so that six end points of the arcs are painted alternately too).

You have an "impossible" blue-green circle.

In fact you can take just one arc (1/6 of circle) and paint it any way you want. Then for each point P of the arc take a regular hexagon H inscribed in the unit circle such that P is a vertex of H, and paint the other 5 vertices of H alternately (regarding color of P). Again you have an impossible blue-green circle.

"Divide unit circle into 6 equal arcs. Paint those arc blue and green alternately (so that six end points of the arcs are painted alternately too)."

Then "all red centered circles" are painted that way. Making 0 deg-green, 60 deg-blue. But the points are alternated so 30 deg is green (even).

Therefore all ends of 60 deg arcs is two colored while all ends of 30 deg arcs is one colored.

If two red centered circles , where one has twice the radius of the other intersects at P2 and P1 ...

P2

r1 60deg 30 deg r2

P1

are P1 and P2 same colored or not ? or 1 is colored cyan?

0 members, 0 guests, 0 anonymous users