Quick
Answer:
The
missing design could be:


Complete
Solution:
One way to approach
this problem is to examine the pattern of dots.
In the first figure, there are four rows of horizontal
dots in the pattern 1, 3, 3, 1. In the third figure, there
are eight rows of dots in the pattern 1, 3, 5, 7, 7, 5,
3, 1. It seems logical, therefore, that the missing figure
would include six rows of dots in the pattern 1, 3, 5,
5, 3, 1
[see pattern at left].
Another way to
look at the pattern is to count the ”loops”
in the design. The first figure has two loops
per side, while the third figure has four loops per side.
In this case, it seems reasonable for the missing figure
to have three loops on each side.
A third way to
consider the problem involves counting squares.
The first design is a twobytwo square; the third is
a sixbysix square. Therefore, the second might be a
fourbyfour square. pattern below so that every dot lies
on at least one of the line segments. 
