New Syllabus

Calendar problem revisited

Here’s a twist on the classic “What day of the week does a particular date fall on?” problem. A programming solution using the following approach would use several simple lookup tables, probably implemented as arrays, lists, or hash maps. I’ve translated the basic idea that I found here (via reddit) into something more appropriate for programming instructors and students.

The result can be calculated using the following formula:

dayOfWeek = (yearCode + monthCode + day) % 7

The result is an integer in the range 0 to 6, interpreted as follows:

As usual, leap year needs to be accounted for. If the date in question is in a leap year, the result should be decremented by one for the months of January and February.

The month code is a non-intuitive integer as follows:

The year code can also be determined using a lookup table, such as:

Or the year code can be computed using the following formula:

yearCode = (centuryCode + twoDigitYear + (twoDigitYear / 4)) % 7

The two digit year value is the last two digits of the year (84 for 1984). The century code follows the 6-4-2-0 pattern below and applies only to dates in the Gregorian calendar.

Happy programming.