Day Finder
On which day of the week did December 31, 1999 fall? Calculate it without a calender.
- Eric
P.S. Show your math; BTW I will be giving the super long and super complicated answer on friday
- Eric
P.S. Show your math; BTW I will be giving the super long and super complicated answer on friday
Labels: mathemagic, SharedPuzzle
posted by Mr Fahrenheit at
5:46 PM
17 Comments:
tuesday? random guess. it just sounds right to me.
o<-< stick man
yay first post
3xLfeb 3x28 = 3x0 = 0mod7
6xNfeb 6x27 = 6x6 = 1mod7
(8x7+1)Jan 57x31 = 1x3 = 3mod7
8x4xApr 32x30 = 4x2 = 1mod7
today is March 13 = 6mod7
total days past 4mod7
today is Thursday
Dec 31,1999 was a Sunday
then I check the historical record and
well my mistake must be obvious but I can't find it.
the pattern is 1112
Count backwards
dec/31/2007 was monday
I'm not giving any more hints.
There were 8 years between 12/31/99 and 12/31/07 which would leave 12/31/99 to fall on Sunday if there were no leap days. There were 2 leap days between the 2 dates which leaves 12/32/99 to fall on Friday.
***12/31/99 not 12/32/99 lol my bad
I was about to say. The only month with 32 days is the now-obsolete 102nd month Centember.
***EDIT: I forgot about Braduary, during a tricentennial Thrust Year. sry***
HHMMMMMM/by/using/the/ almighty/power/mmmmmmm/i/
tell/ye/of/little/faith/mmmmmmmmmm/that/december/
thirty-first/mmmm/nineteen-ninety-nine/mmmmmmmm/was/
indeed/a/friday/mmmmmmm/
mandi/you/are/correct/just like/
Thomas
HHMMMMMMsorry/about/that/mmmmmmmwhat/i/meant/to/say/was/mmmmmmmmmm/by/using/the/ almighty/power/mmmmmmm/i/
tell/ye/of/little/faith/mmmmmmmmmm/that/december/
thirty-first/mmmm/nineteen-ninety-nine/mmmmmmmm/was/
indeed/a/friday/mmmmmmm/so/
mandi/you/are/correct/just/like/me/mmmmmmmm
Thomas
I thought that Y2K wasn't worth worrying about. LOL
Today is Friday 3/14/08
Jan 08 = 31 days
Feb 08 = 29 days (2008 is aleap year)
Mar 08 = 14 days (only up to today)
Total Days of 2008: 74
Total Days of 2007: 365
Total Days of 2006: 365
Total Days of 2005: 365
Total Days of 2004: 366 (leap year)
Total Days of 2003: 365
Total Days of 2002: 365
Total Days of 2001: 365
Total Days of 2000: 365 (not a leap year)
Total Days of 1999: 1 (which is 12/31/1999)
==========================================
8 years * 365 days = 2920
+ 1 leap day in 2004 = 2921
+ 74 days of 2008 = 2995 (includes a leap year)
+ 1 day of 1999 = 2996
2995 / 7 = 428 with Remainder 0
so the day of the week is the same as today (Friday).
had it been remainder 1 would have been saturday
remainder 2 for sunday, etc
Today being March 17, 2008; I'll go form here:
88 Days ago was
Dec 31,2007 = Monday
-dec 31, 2006= Sunday -365
-dec 31, 2005= Saturday-365
-dec 31, 2004= Thursday-366
-dec 31, 2003= Wednesday-365
-dec 31, 2002= Tuesday-365
-dec 31, 2001= Monday-365
-dec 31, 2000= Saturday-366
_dec 31, 1999= Friday
Euclid's Brother Question to you? Y is 2000 not a leap year?
The first anonymous guy put forward a pretty good clue: 1112. (also that 12/31/07 was a Monday; I had to count to be sure though)
Now you COULD do some long equations with 365/366, but you may as well just strip it down right there:
365/7=52R1
That is - there are 52 weeks, 1 day in an ordinary year. But really it's just that 1 day that you have to pay attention to; it means that 12/31 is a day later every year, unless that year is divisible by 4 - in which case it's a leap year/year the summer olympics are held/year of a U.S. presidential election in case you non-americans didn't know but how couldn't you since we can't and won't stop honking about it - and it is two days later. So really, just go backwards through the week accordingly:
2007: Monday
2006: Sunday
2005: Saturday
2004: Friday, Thursday
2003: Wednesday
2002: Tuesday
2001: Monday
2000: Sunday, Saturday
1999: Friday
to answer poser of querys question:
a leap year is every four years because the year is actually 365 days and 6 hrs long so they add a day every 4 years. but this still has a flaw. the year has to be divisible by 400, if it isnt divisible by 400 then you cant have a leap year e.g. 2000. julius cesar came up with all this.
o<-< stickman
It is obviously. I worked that out by having a sly peek at the question;searching for the only day in there, which was Friday. gosh, aren't i smart? lol
From that nauseating potluck of data, Wikipedia:
The Gregorian calendar system dropped 10 days to bring the calendar back into synchronization with the seasons and, to keep it there, adopted the following leap year rule:
Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100; the centurial years that are exactly divisible by 400 are still leap years. For example, the year 1900 was not a leap year; the year 2000 was a leap year.
In the Julian calendar, all years exactly divisible by 4 are leap years.
As clarification, too - if you're reading this, chances are you use the Gregorian calendar.
It falls on a friday :) (just a guess)
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