Arrange 7 Points in a Plane...Date: 10/05/98 at 10:28:09 From: Steve Lesko Subject: A problem you will never get in 3*10e99 years Arrange 7 points in a plane so that if any three are chosen, at least 2 of them will be a unit distance apart. I got this problem from the USA Math Talent Search, which is sponsored by the NSA, so there must be an answer. Date: 10/05/98 at 12:01:17 From: Doctor Rob Subject: Re: A problem you will never get in 3*10e99 years There must be more to this problem than this. Arrange them in a row with 2 units between each adjacent pair. - Doctor Rob, The Math Forum http://mathforum.org/dr.math/ Date: 10/05/98 at 19:05:31 From: Anonymous Subject: Re: A problem you will never get in 3*10e99 years You have to be able to pick any 3 and have 2 of the points a unit apart. The closest I have come is with 6 points, and it's a square ABCD, with equilateral triangles ABE and CDF, and F and E are a unit apart, but there isnt a 7th point that can be added and have it fulfill the requirements. I didn't understand the problem at first either. Date: 10/08/98 at 10:58:37 From: Doctor Rob Subject: Re: A problem you will never get in 3*10e99 years Draw a rhombus made up of two equilateral triangles joined together along a side. Now draw a second one. They contain eight points, so take one of the sharp points of each rhombus and make them coincide. You get a figure like this: A o / \ / \ o-----o \ / \ / B o / \ / \ o-----o \ / \ / C o where all the lines have length 1 unit. The only triple of points that doesn't include a pair 1 unit apart are {A,B,C}. Now rotate the lower rhombus about point B until points A and C are exactly one unit apart. - Doctor Rob, The Math Forum http://mathforum.org/dr.math/ Date: 10/08/98 at 21:16:26 From: Anonymous Subject: Re: A problem you will never get in 3*10e99 years THANK YOU so much for that answer. |
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