Now then, I seek an internal pattern, not really the detailed answer. Because I am pressed for time.
So how would a highly logical person attack this problem?
Suppose the Calender were only 28 days per month for the 12 months. Suppose 1 January 2013 was a Monday. Then the 1st of every month would be Monday also. So that the 2nd Wednesday of every month would be a constant 10 day wait.
But now suppose the Calendar had 29 days to January, 28 for February, 29 for March and alternating similar to the alternation of 31 to 30 days in the usual calendar. How would that affect the constant pattern of 10 day wait? Well, if January started 1st as Monday and had 29 days then February 1st would be Tuesday and since it has 28 days, March 1st would be Tuesday also, but since March has 29 days, April 1st would be a Wednesday. So the internal pattern for a 29 alternating with 28 days is that we have ONE Monday being the first of the month, TWO Tuesdays being the 1st day of the month, TWO Wednesdays being the first of the month, etc.
So the internal pattern of the normal calendar is that we can expect TWO Wednesdays being the 1st of the Month in any random calendar year.