Mental Math Tricks — Find the Day of the Week a Given Date Falls On


The ability to know what day of the week a given date falls on is usually associated with savants. But with a little memorization and some arithmetic, anyone can do the same. There are several techniques, some requiring more memorization than others, some requiring more arithmetic. The technique in this post requires memorizing 12 single-digit numbers for the year you’d like to use it on, but it requires less calculation than alternative methods (such as this one).

Before you amaze your friends, you’ll need to do a little preparation. First, find the 12 dates for the first Sunday in each month. In 2013, those dates are the 6th, the 3rd, the 3rd, the 7th, the 5th, the 2nd, the 7th, the 4th, the 1st, the 6th, the 3rd, and the 1st. Once you have the dates, memorize them. Personally, I prefer to memorize them in four groups of three: 633, 752, 741, and 631. You can memorize them by brute force or with a mnemonic. I use the major system as a mnemonic, which turns numbers into more memorable words.

When you’ve been given a date during the same year and you want to know what day of the week it falls on, recall the date of the first Sunday in that month. This is where memorizing four groups of three makes the job a little easier. Each group represents the months in a particular season. The first group of three are the three winter months, the second group are the spring months, and so on. June is the last month of spring, and spring’s group is 752, so the first Sunday in June fell on the 2nd.

Once you have the date of the first Sunday in the month, subtract that date from the date you’ve been given. If you’re looking for the day of the week that June 28 fell on, and the first Sunday in June fell on the 2nd, subtract 2 from 28, meaning there were 26 days between the first Sunday in June and the 28th. If you’re using a date before the first Sunday and subtracting gives you a negative number, just add 7 to the result and keep going.

Finally, divide the number of days between the first Sunday and the given date by 7, then take the remainder. 26 days divided by 7 is 3 remainder 5, meaning June 28 was 5 days from the previous Sunday, so June 28 fell on a Friday.

With a little practice, you can quickly calculate the day of the week that any date of the year falls on. In my experience, you only really need to know dates for the current year, and as winter approaches, the coming year.

If you’d like to cut down on how many numbers you have to remember for a given year, you can derive a couple with some additional facts:

  • The first Sunday in November falls on the same date as the first Sunday in March.
  • The first Sunday in March falls on the same date as the first Sunday in February except on leap years when the date of the first Sunday in March is one day earlier than the first Sunday in February.

If you have any other mental math tricks, I’d love to hear them!