does anybody know how to calculate the days of the week in your head ?

Question

the formula should be easy to remember, of course.

ta

p`haps i wasnt clear... you know when some clever people are asked "what day is the 20th of august 1965" and they can work out the answer... HTF do they do it ??

Answer 1

August 20th, 1965 was a Friday.

Here's how I arrived at that answer:

Start with the two digit year:
y = 65

Divide it by 7 and take the remainder. So you have 2.

Now add the number of leap years (65/4) = 16, again divide this by 7 and take the remainder. So you have another 2, for a total of 4.

Next we have to add an offset for the century.
1600, 2000 = 0
1700, 2100 = 5
1800, 2200 = 3
1900, 2300 = 1

So the offset is 1 for a total of 5, so far.

Now I memorized a table for the months:
Jan-Mar = 622
Apr-Jun = 503
Jul-Sep = 514
Oct-Dec = 624

August is the middle of 514, or 1.
Add that to our result so far and you have 6.

At this point if it was Jan or Feb in a leap year, you have to subtract 1, but this is not the case...

Finally add the day (20) for a total of 26. Again take mod 7 (divide by 7, keep the remainder). That's 5.

The numbers equate to days as follows:
0 = Sunday
1-5 = Monday - Friday
6 = Saturday

So the answer is August 20th, 1965 was a Friday.

Here's a quick example for today (July 27, 2006).
y = 6
leap years = 6/4 = 1
century offset = 0
Total so far is 7, but you can always just divide by 7 and take the remainder, so this is 0.

Month is July (start of 514) or 5. 5+0 is still 5.
Add the day (24) for a total of 29. Divide by 7 and take the remainder. You have 1.
So today is 1 (Monday).

Another example for 1/1/2000:
y = 0/7 remainder 0
leap years = 0/4 = 0
century offset = 0
January = beginning of 622 = 6
but it was a Jan or Feb in a leap year so subtract 1 = 5
Add the day (1) = 6

So Jan 1, 2000 was a Saturday.

Finally, let's do July 4, 1776
y = 76, mod 7 = 6
leap year = 76/4 = 19, mod 7 = 5
century offset = 5
Total so far 16, but mod 7 = 2

July is 5 (in 514), so we are at 7 mod 7 = 0
Day = 4, so we are at 4
4 is a Thursday.

Just don't go too far back because the Gregorian calendar was adopted in September 1752, so any earlier and you'd have to learn the Julian calender which is different. Fortunately if you are doing birthdays and events in recent history, you shouldn't have this problem.

In summary:
8/20/1965 = (5) Friday
7/24/2006 = (1) Monday
1/1/2000 = (6) Saturday
7/4/1776 = (4) Thursday
If you practice you can do this all in your head rather quickly.

Answer 2

The simplest general formula is as follows.

W = {k + [2.6m - 0.2] - 2C + Y + [Y/4] + [C/4]} mod 7

k is the day of the month
m is the month, with March = 1, April = 2, etc. up to February = 12.
Y is the two-digit year. !! January and February must be counted as belonging to the previous year !!
C is the century.
[..] stands for rounding down; mod 7 is the remainder after dividing by 7.

The outcome W is the day of the week, with Sunday = 0, Monday = 1, ..., Saturday = 6.

Example: August 20, 1965 has k = 20, m = 6, Y = 65, C = 19.

W = {20 + [2.6*6 - 0.2] - 2*19 + 65 + [65/4] + [19/4]} mod 7
W = {20 + 15 - 38 + 65 + 16 + 5} mod 7
W = 83 mod 7 = 6 --> Saturday


I know, I know... still too cumbersome to do in your head... Those people you talk probably remember some dates and go from there. Here is a trick: when going backward or forward a year, the weekdays decrease and increase by 1, or by 2 if you pass a leap day.

For instance, once I know that August 20, 1965 is a Saturday, I can quickly conclude that August 20, 1964 was a Friday, the same date in 1963 was a Wednesday, etc.

Answer 3

It's relational. Some people can take a given date with a known day and mentally look ahead or back, counting the dates in between in order to arrive at the correct day of the week. I'm sure it can be expressed mathematically, but I'm not sure how. It's generally regarded as a "savant" ability, as far as I know.

Answer 4

I have no idea how one can "calculate" days of the week. What on earth are you talking about????

Answer 5

No - but there must be a trick to it.

Answer 6

uhhhh...ok

Answer 7

???? monday ... sunday,