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?
This is the second part.
I am assuming, that the distances are measured around the circumference.
Use AF to signify each of the points.
The distances I used are below
AB = 1
BC = 2
CD = 4
DE = 5
EF = 8
FA = 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 20040815 10:39:44 