How to Determine the Day of the Week for August 10th When There Are Three Friday the 13ths in a Year

Trying to calculate the day of the week for an arbitrary date can be a challenging task, especially when there are unique calendar patterns such as three occurrences of Friday the 13th in a single year. Recently, I found myself pondering over when August 10th of that same year would fall on, given the presence of three Friday the 13ths. Initially, I relied on my 'old grey wrinkled brain' (OGWB) to solve the puzzle, but the result was incorrect. In the end, I turned to technology for assistance. Below, I provide a detailed explanation of the solution and share some insights into the unique calendar patterns that can occur.

Verifying the Calculation Using Excel

Excel is a powerful tool for tackling such problems, and it can be used to determine the day of the week for any given date. First, you need to set up your cells to display the day of the week in a readable format. Here's how you can do it:

Open Excel or Google Sheets and input the dates you're interested in. Select the cells where you've entered the dates and format them by going to Format Cells > More number formats > Custom. Under the Type field, input the format as {dddd dd mmm yyyy}. Hit OK to apply the formatting.

For example, to find out when August 10th falls on a Monday or Friday, you can input the following dates and use Excel to verify the result:

Common Year Scenario

Let's assume there are three Friday the 13ths in a common year. The only common year scenario where this happens is when February has a Friday the 13th. Therefore, the day of the week for August 10th in a common year would be a Monday.

To verify this, you can use the EOMONTH function in Excel to find the last day of the month before August and then add the appropriate number of days to determine August 10th. Here's an example:

TEXT(EOMONTH(YEAR(A1),1) 22, "dddd dd mmm yyyy")

Replace A1 with the cell containing the year format, and it will output the date 'Monday 10 Aug 2015'.

Leap Year Scenario

A leap year scenario where three Friday the 13ths occur is when January has a Friday the 13th. In such a case, August 10th would fall on a Friday.

Using the same approach, you can set up a similar formula to verify this:

TEXT(EOMONTH(YEAR(A1),1) 21, "dddd dd mmm yyyy")

This will output 'Friday 10 Aug 2012' in this example.

Understanding the Calendar Patterns

There are specific patterns in the calendar that allow for three Friday the 13ths to occur in a year:

Leap Year Scenario

For a leap year, the only possible three-way occurrence of a Friday the 13th is in the months of January, April, and July. If any one of these months has a Friday the 13th, the other two will also have a Friday the 13th, and hence, August 10th in that year will be a Friday. An example of a leap year with three Friday the 13ths is 2012 or 2040.

Common Year Scenario

For a common year, the only three-way occurrence is in the months of February, March, and November. If these three months share a Friday the 13th, then August 10th that same year will be a Monday. An example is the year 2015.

Conclusion

Whether you're dealing with a common year or a leap year, understanding these unique calendar patterns can help you determine the day of the week for August 10th. By using Excel or Google Sheets to format cells and apply the necessary formulas, you can easily derive the correct answer to such a challenging question. The key is to recognize the specific calendar configurations that allow for three Friday the 13ths and then apply basic date calculation techniques to determine the day of the week for the date in question.