You can figure the day of the week corresponding to any date from about 1583 AD by a method that is a little involved, but easy to remember. There are some things you must know:
If you are going to figure days of the week only in the twentieth and twenty-first century, you can forget this first rule: Century years 1700, 1800 and 1900 are not leap years. A century year must be divisible by 400, not just 4, to be a leap year.
You must know the number of days in each month. If you don’t know them already, almost by second nature, you probably never will, so you won’t be able to use this method.
You must remember that January 1, 2000 was a SATURDAY.
There are a couple of easy-to-memorize patterns. Taking the four quarter-points of the year, January 1, April 1, July 1 and October 1, we have two patterns:
Pattern A: In a non-leap year, if January 1 is Tuesday, for example, the four days are Tuesday-Monday-Monday-Tuesday. If it’s Friday, the days are Friday-Thursday-Thursday-Friday, and so forth. January 1 and October 1 are the same; April 1 and July 1 are one day earlier. Once you’ve read and understood, you’ll probably never forget.
Pattern B: In a leap year, if January 1 is Tuesday, the four days are Tuesday-Tuesday-Tuesday-Wednesday. What could be easier?
Now say you want to know the day of the week for August 5, 1937. Here’s how you proceed:
Subtract 1937 from
Next, take the first leap year you come to starting with the year in question. If you’re in 1936, the first leap year is 1936. If you’re in 1937, the first leap year is 1940. Subtract the leap year from 2000, and divide by
We add the abovesaid 63 and 15 to get 78. Take the highest multiple of 7 that is less than that figure and subtract it. So we subtract 77, which is 11 x 7, from 78, and we get 1.
That means that January 1, 1937 was one day of the week earlier than January 1, 2000. So it fell on Friday.
Now applying Pattern A, since 1937 was non-leap, we see that July 1 was Thursday. July has 31 days, which is 3 days over four weeks. So we move up 3 days. We say, “July 1 was Thursday. August 1 was Friday-Saturday-Sunday.”
Once we know August 1 was Sunday, we can count on our fingers or in our head, and find that August 5, 1937 was Thursday.
For a day in the twenty-first century, say September 7, 2007, proceed thus:
Subtract 2000 from 2007 and get 7. Remember that for a moment.
Then take the first leap year starting with your year. For 2004, take 2004. For 2005, 2006 or 2007, take 2008. Subtract 2000 from the leap year and divide by 4. So, 2008 minus 2000 is 8; dividing 8 by 4, we get 2.
Now add 7 and 2 to get 9. Then subtract the highest multiple of 7, which is 7 itself in this case. So our final answer is 2. That means that the day of the week for January 1, 2007 was 2 days later than January 1, 2000. Therefore, it was Monday.
Applying Pattern A again, we see that July 1, 2007 was Sunday. July and August both have 31 days. So we have to go up three days for each month. We say, "July 1 was Sunday. August 1 was Monday-Tuesday-Wednesday. September 1 was Thursday-Friday-Saturday."
Since September 1 was Saturday, so was September 8. Therefore, September 7 was Friday.
I devised Patterns A and B, because it would be too difficult to remember a pattern for 12 individual months. But without some kind of pattern, it would be hard to figure out the late months in the year. You’d have to count all the way from January.