It has been conjectured ( astro-ph/0103463 ) that a gravitational lens consisting of n point masses can not produce more than 5 ( n - 1 ) images as is known to be the case for n = 2 and 3 .
The reasoning is based on the number of finite limit points 2 ( n - 1 ) which we believe to set the maximum number of positive images and the fact that the number of negative images exceeds the number of positive images by ( n - 1 ) .
It has been known that an n -point lens system ( n \geq 3 ) can produce ( 3 n + 1 ) 
images and so has been an explicit lens configuration with ( 3 n + 1 ) images .
We start with the well-known n -point lens configuration that produces ( 3 n + 1 ) images and produce ( 2 n - 1 ) extra images by adding a small ( n + 1 ) -th mass so that the resulting ( n + 1 ) -point lens configuration has ( 2 n ) discrete limit points and produces 5 n images of a source .
It still remains to confirm in abstraction that the maximum number of positive image domains of a caustic domain is bounded by the number of the limit points .