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Points On A Circle II (Posted on 2010-07-13) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

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Part A - a further reduction | Comment 4 of 12 |
Following Steve's lead and defining the distance between points as the minimum arc length between them, I think I've got the circumference down to 48 by using the following adjacent separations in the order given.

1, 4, 2, 8, 9, 13, 11

so that the 21 unique distances are:

1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,22,23,24

Ths would give a radius of 24/pi, but is this the smallest?
  Posted by Harry on 2010-07-14 00:40:11
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