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Points On A Circle (Posted on 2004-08-14) Difficulty: 4 of 5
I placed six points on the circumference of a circle such that the distance between any two of the points is an integer. What is the smallest such circle I could use?

What if each distance must be unique?

No Solution Yet Submitted by ThoughtProvoker    
Rating: 4.4286 (7 votes)

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Solution An assumption, and a start. | Comment 2 of 17 |
This is the second part.

I am assuming, that the distances are measured around the circumference.

Use A-F to signify each of the points.

The distances I used are below

A-B = 1
B-C = 2
C-D = 4
D-E = 5
E-F = 8
F-A = 21

from this we can produce the following table to check for no duplicates, all directions for values are the same.

     A     B     C     D     E     F
A   *     1      3     7     12   20
B  40    *      2     6     11   19
C  38   39     *     4     9     17
D  34   35    37    *      5    13
E   29   30    32   36     *     8
F   21   22    24   28    33    *

As you can see, there are no duplicates.

The circumference for the above circuit is 41units, this means the circle is 13.0507units in diameter.

Edited on August 15, 2004, 10:41 am
  Posted by Juggler on 2004-08-15 10:39:44

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