wu :: forums « wu :: forums - 7 points in a plane » Welcome, Guest. Please Login or Register. Sep 25th, 2018, 9:58am RIDDLES SITE WRITE MATH! Home Help Search Members Login Register
 wu :: forums    riddles    medium (Moderators: Icarus, towr, Eigenray, SMQ, william wu, Grimbal, ThudnBlunder)    7 points in a plane « Previous topic | Next topic »
 Pages: 1 Reply Notify of replies Send Topic Print
 Author Topic: 7 points in a plane  (Read 1933 times)
thedkl
Newbie

Posts: 18
 7 points in a plane   « on: Mar 13th, 2007, 4:46am » Quote Modify

draw 7 points on a 2d plane such that for every 3 of them there is a pair of a 1 unit distance
 IP Logged
towr
wu::riddles Moderator
Uberpuzzler

Some people are average, some are just mean.

Gender:
Posts: 13640
 Re: 7 points in a plane   « Reply #1 on: Mar 13th, 2007, 5:49am » Quote Modify

I half suspect there isn't a solution.
 IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
Grimbal
wu::riddles Moderator
Uberpuzzler

Gender:
Posts: 7408
 Re: 7 points in a plane   « Reply #2 on: Mar 13th, 2007, 7:14am » Quote Modify

I also half suspect.  Does it make it certain?
 IP Logged
towr
wu::riddles Moderator
Uberpuzzler

Some people are average, some are just mean.

Gender:
Posts: 13640
 Re: 7 points in a plane   « Reply #3 on: Mar 13th, 2007, 7:49am » Quote Modify

I just found a solution.

Say a connects to b,c,d,e; b and c connect to f; d and e to g; and f and g are connected. Also b connect to c, and d connects to e.[/edit] (Where a connection means there's a distance of 1 between them)

There may be more solutions, but this was enough work.
 « Last Edit: Mar 13th, 2007, 9:40am by towr » IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
Grimbal
wu::riddles Moderator
Uberpuzzler

Gender:
Posts: 7408
 Re: 7 points in a plane   « Reply #4 on: Mar 13th, 2007, 7:57am » Quote Modify

Damn, you are right.  Congratulations!

Note that I haven't changed my mind ... I still think you are right.
 IP Logged
rmsgrey
Uberpuzzler

Gender:
Posts: 2818
 Re: 7 points in a plane   « Reply #5 on: Mar 13th, 2007, 8:33am » Quote Modify

on Mar 13th, 2007, 7:49am, towr wrote:
 I just found a solution.   Say a connects to b,c,d,e; b and c connect to f; d and e to g; and f and g are connected. (Where a connection means there's a distance of 1 between them)   There may be more solutions, but this was enough work.

d,e,f?
b,c,g?
Any three of b,c,d,e?
 IP Logged
SMQ
wu::riddles Moderator
Uberpuzzler

Gender:
Posts: 2080
 Re: 7 points in a plane   « Reply #6 on: Mar 13th, 2007, 8:35am » Quote Modify

I came up with the same solution (all colored links are unit length):

--SMQ
 IP Logged

--SMQ

rmsgrey
Uberpuzzler

Gender:
Posts: 2818
 Re: 7 points in a plane   « Reply #7 on: Mar 13th, 2007, 8:50am » Quote Modify

Ah, the solution was incompletely specified...

There's (at least one) configuration that has only the links towr mentioned unit length, and not the additional pair of links...
 IP Logged
SMQ
wu::riddles Moderator
Uberpuzzler

Gender:
Posts: 2080
 Re: 7 points in a plane   « Reply #8 on: Mar 13th, 2007, 8:51am » Quote Modify

on Mar 13th, 2007, 8:33am, rmsgrey wrote:
 d,e,f? b,c,g? Any three of b,c,d,e?

Are you interpreting tha problem statement the same way as the rest of us?  I read it as: plot 7 points in a plane such that for any three chosen points, at least one pair of points is exactly a unit distance apart.

Edit: Ah, I see, towr forgot to mention the b-c and d-e links...

--SMQ
 « Last Edit: Mar 13th, 2007, 8:54am by SMQ » IP Logged

--SMQ

towr
wu::riddles Moderator
Uberpuzzler

Some people are average, some are just mean.

Gender:
Posts: 13640
 Re: 7 points in a plane   « Reply #9 on: Mar 13th, 2007, 9:38am » Quote Modify

on Mar 13th, 2007, 8:51am, SMQ wrote:
 Edit: Ah, I see, towr forgot to mention the b-c and d-e links...
Indeed. I'll go edit them in..

Are there other solutions? I had some 1100 possible solutions left, when I tried a random one to see if it was an actual solution.
 IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
Eigenray
wu::riddles Moderator
Uberpuzzler

Gender:
Posts: 1948
 Re: 7 points in a plane   « Reply #10 on: Mar 13th, 2007, 2:27pm » Quote Modify

This graph is called the Moser spindle; it cannot be 3-colored, and so it is impossible to color the points of R2 with 3 colors such that no two points a unit distance apart are the same color.  It can, however, be done with 7 colors, so the chromatic number of the plane is somewhere between 4 and 7, inclusive.  (Even though these bounds are easy to prove, they are still the best known after more than 50 years!)
 IP Logged
Altamira_64
Junior Member

Posts: 116
 Re: 7 points in a plane   « Reply #11 on: Apr 12th, 2017, 6:31am » Quote Modify

How about 8 points? Is there a solution?
 IP Logged
 Pages: 1 Reply Notify of replies Send Topic Print

 Forum Jump: ----------------------------- riddles -----------------------------  - easy => medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »