Refer to Points On A Circle.

(A) Seven points are placed on the circumference of a circle such that the distance between any two of the points, measured along the circumference, is an integer.

What is the smallest radius of the circle, given that each of the distances is unique?

(B) Seven points are placed on the circumference of a circle such that the distance between any two of the points, measured as a straight line, is an integer.

Determine the smallest radius of the circle. What is the smallest radius of the circle, given that it is rational?

Note: In Part (B) each of the distances may or may not be unique.

(In reply to re(2): Part A - a further reduction by Harry)

I confirmed your set (1, 3, 2, 7, 10, 11, 14). 48 then is the smallest presented circumference so far. And the circle for such is, as you stated earlier, 24/pi (or approximately 7.639437).

Of the 56 that contain diametrically opposite points, in my opinion, are contrary to the requirement that the distances are unique. But, I guess the restriction's interpretation can be debated.  

Posted by Dej Mar on 2010-07-15 17:50:47