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wu :: forums    riddles    medium (Moderators: william wu, Icarus, SMQ, ThudnBlunder, Eigenray, Grimbal, towr)    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 3332 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: 13730 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: 7527 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: 13730 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. [edit]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: 7527 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: 2873 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: 2084 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: 2873 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: 2084 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: 13730 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? 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