Going from the beginning of the 20th century to 2014, it was on a Saturday in:
1901
1907
1912
1918
1929
1935
1940
1946
1957
1963
1968
1974
1985
1991
1996
2002
2013
April 20, last fell on a Saturday in 2002 and will again fall on a Saturday in 2013.
April 20, last fell on a Saturday in 2002 and will again fall on a Saturday in 2013.
The 20th of April 1963 was a Saturday.
April 20th 1968 was a Saturday.
Twice, in the US. August 20 will fall on a Saturday in the year 2011 and 2016.
Easter was on April 20 in 1930 and 2003. It will be on April 20 again in 2014.
20 April 1957 was a Saturday.
April 20, 1935 was a Saturday.
April 20, 1912 fell on a Saturday.
June 20, 1970 fell on a Saturday.
August 20 fell on a Saturday in the years 2011, 2016, and 2022. This pattern occurs every six years due to the leap year cycle, which occasionally shifts the days of the week. For future reference, the next occurrence will be in 2033.
For any given date (such as April 20), one out of every seven years it will fall on any given day of the week - at least, that's what happens in the long-term average.