Quickly figuring out what day of the week someone was born

Factual Questions
#1

One of my fiancée’s patient’s is mildly retarted, yet can tell you what day of the week you were born on in under five seconds of telling him what your birthdate is. Is there some trick to this that any of us can learn quickly, or does he possess some special skill?

#2

I suppose knowing what day Janurary the first of each year fell on would help.

#3

It’s actually not that hard. Look here for a quick method (where it says, “standard method suitable for mental computation”).

I still do this to “impress” people - very sad.

#4

That’s not hard to do in under five seconds? Damn!

#5

As a bar bet, I used to tell someone I could determine the day they were born within four days. When the money was on the bar, I would say, “Wednesday” and collect my winnings - and then buy the loser a drink (no sense having a fight about it). I once tried this with one of the patrons at my bar, and he laughed good-naturedly at my lame bar trick, then he told me he would make the same wager, but he would tell me the exact day of the week I was born on if I gave him my birthday. As was said in an earlier post, he did it in, like, five seconds. I was so stunned I let him drink free until he left my bar (about a couple of hours).

#6

I believe there is a long history of “idiot savants” who could carry out extremely complex calculations and had incredible memories but were otherwise retarded.
http://www.science-frontiers.com/sf058/sf058p16.htm
http://www.plim.org/2idiots.html
http://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=“idiot+savant”

#7

To speed things up, remember that in the method linked after the first division by four you can utilize mod 7 arithmetic any time you like.

#8

As the website cited shows, there are algorithms for making such calculations since the calendar is cyclic in nature. The calendar repeats exactly with respect to the day of the week and the date of the year every 28 years. This is because the calendar is on a four year cycle (the leap year cycle) and a seven year cycle and these “even out” every time seven four year cycles and four seven year cycles have run.

The seven year cycle refers to the days of the week; if it were not for the complication of leap year, each January 1st would fall on the day of the week after the last January 1st. Thus: this year New Year’s Day was on a Wednesday. Next year it is on a Thursday. In 2005, though, because 2004 was a leap year and pushed things “out of whack”, January 1st will be on a Saturday rather than on a Friday.

Autistic savants who are able to state the day of the week for any given date within a large span are evidently using their own, idiosyncratic methods, ones which they generally cannot articulate, and other people cannot duplicate. Stephen Jay Gould writes about this at length in Questioning the Millennium and Oliver Sacks writes about in The Man Who Mistook His Wife for a Hat. There he discusses identical twins who could calculate, more-or-less instantaneously, the day of the week for any date within a 40,000 year span. They could also identify nine and ten digit prime numbers just by thinking. These twins appear to have been an influence on the script of the film Rain Man; an incident in that movie where Dustin Hoffman instantly visualizes the number of matches which have fallen on the floor, and divides the number by three, is similar to an incident Sacks describes.

Gould emphasizes that such people appear to do their calculations by “visualization” somehow, a point Sacks also acknowledges; in fact, the twins Sacks discussed were said not to be able to multiply or divide. He also cites a suggestion that such people are able to assign a sequential number to every date (within a 40,000 year span!) then divide by seven and base their answer on the remainder.

#9

My method:

Take date (eg. 13 April 1986)

Count years from 1900 (1986->86) call this Y

Divide by 4 disregarging the remainder (86/4 = 21), call that L.

Look up the month in this table



JAN 0
FEB 3
MAR 3
APR 6
MAY 1
JUN 4
JUL 6
AUG 2
SEP 5
OCT 0
NOV 3
DEC 5
#10

My method:

Take date (eg. 13 April 1986)

Count years from 1900 (1986->86) call this Y

Divide by 4 disregarging the remainder (86/4 = 21), call that L.

Look up the month in this table



JAN 0
FEB 3
MAR 3
APR 6
MAY 1
JUN 4
JUL 6
AUG 2
SEP 5
OCT 0
NOV 3
DEC 5

(April->6) Call that M

Add L + Y + M to the day of the month (21 + 86 + 6 +13)

This addition can be done modulo 7: that is we can disregard whole multiples of 7, as and when we see fit.

For instance,
21 = 3 x 7 equals 0 modulo 7,
86 = (12 X 7) + 2 equals 2modulo 7
6, well 6 equals 6
13 = 7 + 6 equals 6 modulo 7

So the sum is 0 + 2 + 6 + 6 = 14

Again we can disregard multiples of 7, giving us 0

Look this up in this table



0 SUN 
1 MON
2 TUE
3 WED
4 THU
5 FRI
6 SAT

So 13 April 1986 was a Sunday

One caveat, if the date falls in a leap year before the leap day subtract one from the total.

This algorithm is good for dates between 1 Jan 1900 and 31 Dec 2099.
Another example? Today’s date 17 May 2003:

2003->103 (Y=103)
103/4=25 (L = 25)
May->1 (M=1)

103 + 25 + 1 + 17 is the same as
5 + 4 + 1 + 3 is the same as
13 is the same as
6 which corresponds to a Saturday. But you knew that.
(Appypollyloggies for the half-post, above)

#11

Yeah, that seems pretty straight-forward… Dang! I’ll just risk getting punched in the nose with my method, I guess.

#12

There was a terrific bit of television recently (The Discovery Channel?) that explored savant-ism, and research efforts to induce such states in “normal” people.

I’d love to read more if anyone can provide a link.