School-Safe Puzzle Games

## A brain teaser to the end of times

If the earth should suffer an apocalypse on the first day of a new century, can you say what the chances are that it will happen on a Sunday?

Feel free to enter you answer below in the comments section; will reveal submissions before the week is over.

(some new clues are up for Rock Star Rebus)

### 19 Comments to “A brain teaser to the end of times”

1. Shawn | PUZZLE GRANDMASTER | Profile

The chances are zero.

The first day of a new century is 01/01/xx01. A quick check at an online date calculator shows that these dates cycle between Monday (2001), Saturday, Thursday, and Tuesday respectively.

For the few left on the planet who will insist that the century starts on 01/01/xx00, it can be shown that this date will also never be a Sunday, cycling between Saturday, Friday, Wednesday, and Monday.

2. michaelc | Profile

Ahhh…

you might think the answer would be 1/7. But that’s why they call em’ brain teasers.

Actually the turn of a century never happens on a Sunday. There’s a 25% chance that it will be on a Saturday, Friday, Wednesday or Monday.

It’s a repetitive cyle happening every 400 years. For instance, 1/1/2000 was on a Saturday. 1/1/2100 will be on a Friday. 1/1/2200 will be on a Wednesday. 1/1/2300 will be on a Monday. 1/1/2400 will be on a Saturday again and the cycle repeats.

By the time, oh say 1/1/2200 rolls around, we’ll probably be on star dates like Star Trek by then, and the whole concept of days and years will be reinvented. If we haven’t blowed ourselves up with a bunch of nuclear weapons by that time.

There’s a lot of things to worry about in today’s times, but by golly, we don’t have to worry about the world ending on a Sunday at the turn of the century.

3. Scott | Profile

Zero percent chance.

Due to the number of days in a century (36524 or 36525) – as well as the rules for leap years – the days that the first day of a century would only be on Saturdays, Fridays, Wednesdays or Mondays.

Scott

4. Sue | Profile

The chances are 0% that it will happen on a Sunday or Wednesday or Friday. The Gregorian Calendar repeats every 400 years.

5. Gray-T | Profile

based on experience, it always was on a Monday :-D

or I´ll put it like this: god created the world in 6 days, starting on Monday, and had a rest on the 7th, Sunday.
So the last apocalypse might have been beetween Sunday and Monday, because without a pre-apocalypse, god had not had a need at all to create a new one.

;-)

yes, I know, I´ve missed the point, again…

I guess, Suineg, got it in a snap.

6. bilbao | Profile

According to Julian calendar, there were 24 leap years in 17th, 18th and 19th centuries, which consisted of 36524 days. There were 25 leap years in 20th century as year 2000 was leap year and thus 20th century had 36525 days. From now onwards this cycle will keep repeating itself.
First day of 21st century, 01/01/2001 was Monday. For 3 centuries the first day will shift 5 days and the fourth century will shift 6 days.
Then: 22nd century-Saturday; 23rd-Thursday; 24th-Tuesday; 25th-Monday again
There will never be a first day of century on a Sunday (unless days are added or deleted from calendar, as it happened in october 1582)

7. suineg | PUZZLE MASTER | Profile

RK, I have a question, the problem say the first day of a new century, it mean any new century (2100; 2200 ; 2300; to infinity) like a geometric progression???

0% – Centuries never start on a Sunday

9. RK | Founder | Profile

Hi Suineg,
yes, I belive it means any new centure. thanks, RK

10. suineg | PUZZLE MASTER | Profile

Ok, let me try it:
Info:
you have 25 leap years by century, by a milleniun you have 250 leap years, the leap years have 366 days.

the first day of 2008 was a tuesday.
the week has 7 days.
this century has 23 leap years remaining, including 2008
Logic(I guess):
+ 1 century:
23*366+ 69*365= 8418 + 25185 = 33603= 33600 + 3 = tuesday + 3= friday

+ 2 century:
25*366 + 75*365 = 9150 + 27375 = 36525= 36519 + 6 –> friday + 6 = thursday
Now for every new century you have a + 6 days to change the days of the next century so first days of the centuries of this millenium are:
friday; thursday; wednesday; tuesday; monday; sunday; saturday; friday; thursday ;wednesday
the chances for this millenium are 1/10
next millenium:
tuesday;monday;sunday;saturday;friday;thursday;wednesday;tuesday;monday;sunday
2/10
saturday; friday;thursday;wednesday;tuesday; monday;sunday;saturday;friday;thursday
jajaja this is hard; but there is a pattern; every millenium starts three days before the previous millenium;
and the probability is 2/10 if sunday is in the first 3 days of the millenium otherwise is 1/10 so: 1000: sunday 2,9; 2000: sunday 6, 3000: sunday 3,10; 4000: sunday 7;
5000: sunday 4; 6000: sunday 1,8; 7000: sunday 5; 8000; sunday 2,9; 9000: sunday 6; 10000: sunday 3,10
take the first 8 terms of the series:
2/10 (3) ; 1/10 (5) –> now a ponderate rate;
11/10/8; 11/80 this I think is the probability wow what a hard work to a “probably” big mistake jajajaja but cool.

11. suineg | PUZZLE MASTER | Profile

WOW MAYBE I AM FAMILY OF NOSTRADAMUS: “A PROBABLY BIG MISTAKE JAJAJA”. ok however can someone please tell me what is wrong with my reasoning, cause i could not see my error in it.

12. MattHogan | Profile

suineg, I believe you forgot about the leap years that occur every 400 years. Which might cause some problems in that heap of calculations. I could be wrong though, since I didn’t look at your work very thoroughly.

13. suineg | PUZZLE MASTER | Profile

thanks MattHogan, that might be it, because I thought that leap years occur every 4 years without any interruption, the series I propose counts like that, but it seems to be irregularities in the positions of days, jumping some days( sunday included),I think that might because the leap years dont occur every 4 years or because it also occur on some other irregular times like every 400 years; however 4*100= 400 seems like included in my reasoning but maybe its not, cool.

14. michaelc | Profile

I notice some folks, (actually the majority I think), got their start of the century as 1/1/XX01. So I’d guess you’d probably be right, but just me thinking about it, I’d think it’s like 12AM, and 12 PM. at 11:59PM you’re still in PM, but when the clock strikes 12:00 you’re in AM. Same logic with the century deal.

Can someone else explain the difference logic for the XX01 being the turn of the century?

15. michaelc | Profile

Ah, nevermind.

I researched it on wiki. There was no year 0, only 1 BC, and then 1 AD. So the first century was 1AD – 100AD, and so forth.

Maybe there was no 12:00 minute on the first day.

16. suineg | PUZZLE MASTER | Profile

MattHogan gave me a good explanation of what could be wrong, however I review my calculations and I think I took that in consideration, I know something is wrong for the cycling every 400 years, however can someone please tell me what was wrong in my reasoning?

17. michaelc | Profile

Hi Suineg,

Pehaps this will shed some sort of flickering light on the subject…

With a little help from Wiki…

Julian calendars had a leap year every 4 years, but Gregorian calendar corrected the Julian calendar by a little bit. Years that are divisible by 100, are not leap years unless, they are divisible by 400 years. Such as the year 1900 was not a leap year, but the year 2000 is in fact a leap year.

1/1/2001 was on a Monday.
There were 24 leap years, and 76 regular years from 1/1/2001 to 1/1/2101.

24*366 + 76*365 = 8784 + 27740 = 36524 days

36,519 + 5 = 5217 weeks and 5 days. 1/1/2101 was on a Saturday.

Same scenario from 1/1/2101 to 1/1/2201. 1/1/2201 was on a Thursday (Saturday + 5 days).

Same scenario again from 1/1/2201 to 1/1/2301. 1/1/2301 was on a Tuesday.

Different Scenario from 1/1/2301 to 1/1/2401, because the year 2400 is divisible by 400.

25 leap years, 75 regular years.
25*366 + 75*365 = 9150 + 27375 = 36525
5217 weeks and 6 days.

Which means 1/1/2401 is again on a Monday, and the cycle repeats.

Clear as mud?

18. suineg | PUZZLE MASTER | Profile

thanks MichaelC; my error was assuming that in every century you have 25 leap years and 75 normal years; because I did not know that if a year was divisible by 100 but not by 400 is not considered a leap year, cool, everyday is a good time to learn new things thanks.