## Welcome to BrainDen.com - Brain Teasers Forum

 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

# Voronoi Game/Puzzle

14 replies to this topic

Senior Member

• Members
• 1826 posts
• Gender:Female

Posted 21 May 2014 - 01:33 AM

You and an opponent are sharing a regular sheet of paper.  You will play an area game.  Your opponent goes first and marks a single point in the center of the paper.  You will make a mark in a different location and then it is their turn, your turn and so on.  The game continues until you each have four points on the paper.  As this is the "Voronoi Game", the paper is then divided into 8 areas.  An area is created by drawing perpendicular lines between the nearest points (Inspired by Phil's puzzle) until enough perpendicular lines define the area (ensuring that the border defines area that is closest to that receptive point).  Is there a strategy that you can utilize to ensure you have the largest total area at the end of the game?

example game:

• 0

### #2 bonanova

bonanova

bonanova

• Moderator
• 6142 posts
• Gender:Male
• Location:New York

Posted 21 May 2014 - 06:22 AM

Some lines go off the paper and others terminate on other lines.

Is it correct to assume that all lines must terminate either on the paper's edge or a previously drawn line?

But if so, why is there not one line (the first one drawn) that terminates on two paper edges?

Does the strategy entail the order chosen to draw the lines?

Can you make clearer what is meant by "ensuring that the border defines area that is closest to the receptive point."

Thanks. It sounds interesting.

Edit:

OK I think I get it.

1. The points uniquely determine the lines, which are not part of the strategy.
2. Cells that surround each point comprise the points closer to it than to any other point.
3. The strategy comes in placing your points.

Edited by bonanova, 21 May 2014 - 06:35 AM.
I think I understand my questions

• 0

Vidi vici veni.

Senior Member

• Members
• 1826 posts
• Gender:Female

Posted 21 May 2014 - 01:37 PM

Some lines go off the paper and others terminate on other lines.

Is it correct to assume that all lines must terminate either on the paper's edge or a previously drawn line?

But if so, why is there not one line (the first one drawn) that terminates on two paper edges?

Does the strategy entail the order chosen to draw the lines?

Can you make clearer what is meant by "ensuring that the border defines area that is closest to the receptive point."

Thanks. It sounds interesting.

Edit:

OK I think I get it.

1. The points uniquely determine the lines, which are not part of the strategy.
2. Cells that surround each point comprise the points closer to it than to any other point.
3. The strategy comes in placing your points.

The edge of the paper are the limits of the finite total area and the points split this area up into 8 distinct smaller areas.  Each area is closer to its point than any other point.

Edited by BMAD, 21 May 2014 - 01:40 PM.

• 0

### #4 bonanova

bonanova

bonanova

• Moderator
• 6142 posts
• Gender:Male
• Location:New York

Posted 24 May 2014 - 11:15 PM

Spoiler for First thoughts

• 0

Vidi vici veni.

### #5 m00li

m00li

Junior Member

• Members
• 71 posts

Posted 25 May 2014 - 02:06 AM

Spoiler for My guess

• 0

### #6 plasmid

plasmid

Senior Lolcat

• VIP
• 1483 posts
• Gender:Male

Posted 25 May 2014 - 06:33 AM

Spoiler for My guess

Spoiler for counterexample

• 0

### #7 m00li

m00li

Junior Member

• Members
• 71 posts

Posted 25 May 2014 - 09:57 AM

Spoiler for My guess

Spoiler for counterexample

and I concede defeat

• 0

### #8 plasmid

plasmid

Senior Lolcat

• VIP
• 1483 posts
• Gender:Male

Posted 25 May 2014 - 03:46 PM

Spoiler for strategy for player 2

• 0

Senior Member

• Members
• 1826 posts
• Gender:Female

Posted 25 May 2014 - 04:22 PM

Spoiler for strategy for player 2

How can you mirror player 1's first move in the center of paper?
• 0

### #10 plasmid

plasmid

Senior Lolcat

• VIP
• 1483 posts
• Gender:Male

Posted 25 May 2014 - 07:50 PM

Spoiler for strategy for player 2

How can you mirror player 1's first move in the center of paper?

If player 1 places their point at (0, 0), place yours at (0, 1/infinity).
• 0

#### 0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users