Since
a year is 52 weeks and a one or two days, rather than 48 weeks, there
must be at four or five times a year that roughly three weeks rather
than two pass between the first Wednesday and third Tuesday or vice
versa.
When a month begins on a Wednesday, the third Tuesday is the 21st, one day short of three weeks later.
Any
month other than February that begins on a Tuesday ends either on
Wednesday (if 30 days) or Thursday (if 31), and 31-day months that end
on Monday end on Wednesday, forcing the next meeting to the 6th or 7th
accordingly, three weeks and a day later.