How often does July 1 fall on a Monday?

It falls on a Monday every 5th, 6th or 11th year. This is due to days being skipped by leap years. There is a set of 4 pattern. There is a gap of 6 years, then 5 years, then 6 years again and then 11 years, after which the pattern starts at 6 years again. If you take the years during the 20th century that the 1st of July was on a Monday, you will see the pattern, in this case starting at 6 years, from 1901 to 1907, then 5 years to 1912, then 6 years to 1918 then 11 years to 1929, then 6 years to 1935 and so on:

1901

1907

1912

1918

1929

1935

1940

1946

1957

1963

1968

1974

1985

1991

1996