+422 January has the greatest possible number of Saturdays when January 1 occurs on any of the following days of the week except... I think it's Sunday.
+130071 Note that we have the following sequence
1, 8, 15, 22, 29
When the first day is Thursday....the last Saturday is on the 31st
When the first day is Friday......the last Saturday is on 30th
When the first day is Saturday.....the last Saurday is on the 29th
In each case....there will be 5 Saturdays
But when the first day is on Sunday......the next Saturday will fall on the 7th
And we have the following sequence for Saturdays
7 14 21 28
So...only 4 Saturdays when the first day is Sunday...
