sampling a pattern

To whom:
I was wondering what statistical procedure I could use to determine a color pattern.  I have a shower drape with about 50 rows of colored circles, of which there are six colors.  They appear to be in a pattern.  If I were to sample, say, 9 circles at a time in a 3X3—3horizontal and 3vertical—structure, how could I figure out the pattern?  I want to estimate how many samples it would take before trying and compare to actual number of samples to see how many samples it actually takes to determine this pattern.
 
Thanks for your time
-Todd