# Each of the 43 points is placed either inside or on the surface of a perfect sphere.

Each of the 43 points is placed either inside or on the surface of a perfect sphere. If 16% or fewer of the points touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere?

## Answer/Solution

3

### Steps/Work

Maximum number of points on the surface is 16%*43 = 6.88 ... or 6 since it has to be an integer

Now note that if two points form a diameter, they cannot be part of any other diameter.

So in the best case we can pair up the points

We have 6 points, so at best we can form 3 pairs (6).

So, answer is (A)

Now note that if two points form a diameter, they cannot be part of any other diameter.

So in the best case we can pair up the points

We have 6 points, so at best we can form 3 pairs (6).

So, answer is (A)