Tuesday, from this program http://www.extremelysmart.com/diversions/DOWfinder.php
January 4 1962 was a Thursday.
October 4, 1962 fell on a Thursday.
August 4th 1962 was a Saturday
It was a Sunday.
December 4 1957 was on a Wednesday.
December 4 1998 was a Friday.
December 4, 1964 was on a Friday.
December 4 2009 was a Friday.
December 4 2010 was a Saturday.
Sunday
Saturday
December 4, 1967 fell on a Monday.