It depends how often October starts with a Saturday. As there are exactly 7weeks in a normal year, the begining day of the year, and therfore October, will cycle on by 1 day each year. In a leap year the begining day of the following year will have cycled on by 2 days. Therefore every sixth year the pattern repeats.
Incidently there are seven months each year with three repeating days so I really don't understand how the once in every 823 years thing came about.
My sister has just poster the 823 years thing on facebook and although she has done it as a half-joke, some people really believe this chain mail stuff. So I felt compelled to add my own little contribution of rationalisation to the internet. Please proliferate my nicely reasoned explanation just as much as idiots have bombarded you with requests to pass on their hopeless superstitions.
4 years
there 5 sundays,mondays,saturdays in every 200 years
Over the very long average, once for every seven years. And it's "often".
Never.
October 2011, December 2012, March 2014 for starters. In other words, how often does a 31-day month begin on a Saturday? Fairly often.
The odds are exactly 14.5%, which makes the average frequency once per 6.9 years.
Exactly 14% of all Decembers have five of each of Fridays, Saturdays and Sundays.
Every year has more than 5 Fridays, 5 Saturdays and 5 Sundays.
The month of July has 5 Saturdays and 5 Sundays zerotimes in 2012.
Exactly 14.25% of all July 23rds are Wednesdays. 14% are Sundays, 14.5% are Mondays, 14.25% are Tuesdays, 14.25% are Wednesdays, 14.5% are Thursdays, 14% are Fridays, and 14.5% are Saturdays.
There are 14 calendar variations (7 days of the week plus leap years). Some years October will have 5 Fridays, 5 Saturdays, and 5 Sundays. October 1999, 2010, 2021, and 2032 all have 5 Fridays, 5 Saturdays, and 5 Sundays. This looks like an 11 year gap, but October 1988 and 2043 do not have 5 weekends.
March