On 54 Weeks in a Year and Friday the 13th

Circling Friday the 13th date on calendar with...

Circling Friday the 13th date on calendar with marker (Photo credit: Wikipedia)


How many weeks are in a year? 52, right? I found myself thinking about this earlier today. Does there have to be precisely 52 weeks? It seems to me that there should be some variation.

Since there are 365 days in a year simple division by 7 tells us that there are 52.14 weeks in a year. This is almost always rounded to 52 for simplicity, but 52.14 means that there are 52 full weeks and one extra day. With a leap year there is 52 full weeks and 2 extra days.

Are these extra days enough to justify it being called 53 weeks? Commonly it is said that there are 52.14 full weeks in a year, but there must be at least 53 separate weeks. The first and last weeks for this separate week notion would have under 7 days in them to achieve this.

In an extremely rare case there can even be 54 (separate not full) weeks in a year. If is a leap year where January 1st occurs on a Saturday, then the last day will be on Sunday December 31st. Even though the first and last week only have a single day in them, 54 weeks is achieved. This case happens once every 28 years. The last time it did was in 2000 and the next time it will occur is in 2028.

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Another interesting fact about the calendar that probability has revealed to us is that the 13th day of a month is more likely to occur on a Friday than any other day. With leap years and varying amounts of days in months there is a pattern that comes into play. When comparing a large selection of calendars the following was found.

The probability of the 13th day being on each week day is the following.

SUN 14.31%

MON 14.27%

TUE 14.27%

WED 14.31%

THUR 14.25%

FRI 14.33%

SAT 14.25%

The probability of Friday the 13th happening is slightly higher than the 13th landing on any other day. Further, it was found that every year must have at least one Friday the 13th, and the maximum number of times it can occur is 3. This “unlucky” day happens more often than you might expect it to.


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