Did my kid memorize the whole calendar?

Factual Questions
1

My 9-year old kid can tell you the day of the week for any day on this year. He’s right about 95% of the time (we tested this wi family member last weekend) and when he’s wrong he’s always right on the second try.

Our maid has the theory that he meorized the calendar because last year he had a big calendar in his room and he could tell you the day of the week on that year. For this year, interestingly enough, he only “learnt” the days after going to school where there are calendars everywher.

He doen’t seen to perform any calculations, he repeats the date “March 15th” and says “Thursday”.

Could he have memorized it? What mental trick can a 9-year old use?

He had severe language problems. He didn’t speak a word until almost 3 years old and after 4 years of therapy and 3 years at a specialized school he’s at the middle of the curve for he age in language school. He’s now at regular school.

2

I’m sure that there’s more than one way to do this, but one approach is given in this Car Talk puzzler answer.

3

My brother told me that’s the way he would do it if he wanted to do it, but somehow I don’t think he “cracked” that code on his own because it doens’t look like he add or subtract anything, it’s like he recalls the date.
He says he doen’t know how he does it.

4

He probably just has a special ability in this area. It’s uncommon but not unknown for developmentally delayed individuals to have uniquely strong, narrowly defined, memory abilities. It is particularly associated with autism.

5

Here’s a journal article about a pair of “calendar savants” that suggests that they memorized a set of calendars:

6

Is it possible he is autistic with savant qualities? Take him to a developmental pediatrician.

7

When I was a kid, this is how I did it.

8

Thanks for the answers so far.

We’ve had him tested for everything except ovarian cancer.
He’s definitely dipped his feet in the autism pool (as I probably have, BTW) but he’s not autistic or have Asperger’s.
In his first year in regular school (3rd grade) he finished in the top third almost without any special help.
He only knows (as of now at least) the present year. He doesn’t seem to use a formula.

9

Notice first that these days always fall on the same day of the week in any year (in 2012, on a Wednesday):

Apr. 4, June 6, Aug. 8, Oct. 10, Dec. 12 (or 4/4, 6/6, 8/8, 10/10, and 12/12)

May 9, July 11, Sept. 5, Nov. 7 (5/9, 7/11, 9/5, 11/7 … or: I work 9-to-5 at the 7-11)

also the last day of February, which you can also understand as March 0 (in both common years and leap years)

and in three out of four years Jan. 3, but in leap years (every four years) Jan. 4

So, how do you know which day of the week for a given year?

First, determine the century number. In the 2000s, it’s 2 (like Y2K); in the 1900s it’s 3 (Wednesday is the third day, and “we-in-dis-day” … ahem, most of us were born in the 1900s. If you weren’t, I guess your eff’ed.) There are other values for 1800 or 2100 and so on.

Next, determine how many full dozens of years have elapsed between 1900 or 2000 (or 1800 or 2100 and so on), inclusive. 2015? Then its 1. 2012? Also 1. 2004? 0. 2070? 5.

Then determine the remainder mod 12. So, 2015? 3. 2012? 0. 2004? 4. 2070? 10.

Then determine how many full quartets are in the remainder. 2015? Remainder ® is 3, no quartets (q), so 0. 2012? r=0, q=0. 2004? r=4, q=1. 2070? r=10, q=2.

Then sum these numbers up:
2015: 2+1+3+0=6
2012: 2+1+0+0=3
2004: 2+0+4+1=7
2070: 2+5+10+2=19

And take them mod 7
2015: 6 mod 7 = 6
2012: 3 mod 7 = 3
2004: 7 mod 7 = 0
2070: 19 mod 7 = 5

0 = Sunday (none-day)
1 = Monday (one-day)
2 = Tuesday (obvious)
3 = Wednesday (Threes-day kinda of sounds like Wednesday, right?)
4 = Thursday (Do.)
5 = Friday (Do.)
6 = Saturday (Six-urday, again, basically the same word!)

A trick, if you add in the offset between the day of interest and the appropriate day on the list I opened with before you take the sum mod 7, you will get the day of the week for your day of interest.

So, when is Apr. 12, 2012?

Offset for Apr. 4 = +8
Century number = 2
Dozens = 1
Remainder = 0
Quartets = 0

Sum = 11
11 mod 7 = 4

Thursday.

10

Alternatively, its pretty trivial to memorize the day of the week of the first day of the month for the twelve months of the year and then figure out the day of the week of any other day from there. That takes neither any great feat of computation or memorization and the computation can be done in a second.

But in any case, kids that age seem especially fond of magic tricks and such. I suspect he knows how he does it and just enjoys mystifying you.

11

Mine is way more bad-ass though. I’ll take on any nine-year-old twerp too. And I won’t need two guesses.

12

He was actually lives life in reverse, and is simply remembering that day.

13

Have you tried simply asking him? Tell him that it’s a neat trick that he’s doing, and ask him to teach it to you.

14

That’s the method I learned as a kid. It’s pretty easy to get the pattern down, and then obviously, the 1st, 8th, 15th, 22nd, and 29th of the month are the same day of the week.

15

I’ve asked, begged, bribed, and threatened and the only answer I get is “I don’t know how, I just do it”.

16

Oh! I thought he could name any day to ANY calendar date.

It’s possible he has an unusually strong visual memory and can “see” the correct positions based on having seen the poster so many times.