This tag is for questions about combinatorial and computational issues with regards to calendar systems. A typical, well-known mathematical result in this direction is John Conway's Doomsday Algorithm for computing the "day of the week" associated to a given date.

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25
votes
5answers
4k views

Prove that every year has at least one Friday the 13th

Everyone knows Friday the 13th is regarded as a day of bad luck. Why does every year have at least one of this bad day?
12
votes
2answers
321 views

Formula for occurrence of leap years in the Jewish calendar

Over at Judaism.SE, there was a discussion about a formula to determine leap years in the Jewish calendar. Basically, the calendar follows a 19-year cycle, and seven of those years -- 3, 6, 8, 11, 14, ...
11
votes
1answer
583 views

Weekend birthdays

My birthday this year (2011) is on a Friday. In most years, one's birthday the following year is on the subsequent day of the week, and in that pattern, my birthday next year (2012) it is on a ...
11
votes
3answers
3k views

Calculate which day of the week a date falls in using modular arithmetic

In Summer Wars the main character (he is a mathematician) calculates the day of the week of someone's birthday (19/07/1992 is Sunday). I know (very) basic modular arithmetic but I can't figure out how ...
6
votes
2answers
193 views

Seasonal changes in hours of daylight

I will post my own answer to this question unless someone else posts the same answer first, but I am curious to know what other points of view might lead to different ways of answering it. ...
5
votes
3answers
3k views

birthday problem - expected number of collisions

There are many descriptions of the "birthday problem" on this site — the problem of finding the probability that in a group of $n$ people there will be any (= at least 2) sharing a birthday. I am ...
4
votes
6answers
163 views

Prove that in each year, the 13th day of some month occurs on a Friday [duplicate]

Prove that in each year, the 13th day of some month occurs on a Friday. No clue... please help!
4
votes
2answers
137 views

Prime number based calendar: how to calculate intermediate values?

I'm trying to define a new [silly] calendar, because there aren't enough of them yet. My calendar, so far, is specified: epoch (orthodox) is the moment the leading edges of the dinosaur-killing ...
3
votes
8answers
6k views

How many odd days are there in 1600 years ? I calculated it but I guess the result is wrong?

I had to calculate the number of odd days in 1600 years. I have read the answer to be equal to 0. But I don't get it to equal to 0. This is the way I am calculating the number of odd days in 1600 ...
3
votes
2answers
184 views

Five Fridays and Sundays on October

How to prove that if you take any 400 consecutive Octobers then exactly 14 % of those years have five Fridays and Sundays?
3
votes
1answer
94 views

Given a day of the week and the day of the month, what is the range of time within which it will uniquely specify a single date?

In other words, given "2 Tues", (e.g. today, 2 July 2013), for how long must I wait until it is Tuesday on a 2nd of the month again? How does this interval change for each week? Is it constant or ...
3
votes
3answers
100 views

Easter Dates Different

Show that there in no natural number $n$ such that, for each year $A$, the years $A$ and $A+n$ have the Easter with the same date. Use a computer program for your proof: A number of programs of Easter ...
3
votes
1answer
212 views

Periodicity of calendar

Let $A$ be the set of days in week, $A = \{Mon,Tue,Wed,Thu,Fri,Sat,Sun\}$, and $B = \{1,2,\dots,31\}$. For each date, we have a pair $(x,y)$, $x \in A$ and $y \in B$. Then we will have an infinite ...
2
votes
1answer
98 views

In a certain year, January had exactly $4$ Mondays and $4$ Fridays. What was the day on $2^{\text{nd}}$ October the previous year?

In a certain year, the month of January had exactly $4$ Mondays and $4$ Fridays. What was the day on Gandhi Jayanti $(2^{\text{nd}}$ October $)$ the previous year? I am not sure how to approach this ...
2
votes
2answers
1k views

Solve for numbers to appear on two six-sided dice

I have a small wooden calendar that uses two six-sided dice to display day of month. One die carries numbers 0, 1, 2, 6, 7, 8 and the other carries 0, 1, 2, 3, 4, 5. The six of course doubles as the ...
2
votes
3answers
94 views

Is there any fast way to get the number of a certain day in a week

I'm realy sorry, if this question is a bit stupid... But this is my first time on mathematics stackexchange. Do you guys now for example, how to know the number of monday in a year?
2
votes
2answers
441 views

Jack's birthday riddle

Anytime each of three consecutive months has exactly four Fridays, Jack's birthday will fall in one of those three months. Which month is that?
2
votes
2answers
208 views

How to find day of a date

As previously there were a method to find the date from the year 1893 to 2032 , which is very difficult to take a list of table always . Is there any other easy way to find the day of any date ?
2
votes
1answer
1k views

Hindu calendar (lunar) to Gregorian calendar

We have to convert the Hindu calendar (the lunar one) to the Gregorian calendar. According to the (Dutch) Wikipedia (sorry for that, but it has more information than other websites), it is based on he ...
1
vote
3answers
2k views

How often will the same date be on the same day of the week?

Is there any pattern in this (e.g. Once per five years)? Is it a sliding window?
1
vote
1answer
90 views

How long would it have taken the Swedes to align their calendar with the Gregorian calendar?

According to http://www.clas.ufl.edu/users/ufhatch/pages/03-Sci-Rev/SCI-REV-Home/Historical-Research/Calendars/gregorian_calendar_history.html "The Swedish dithered. In 1700 they began what was ...
1
vote
3answers
622 views

What is the probablity of January having 5 sundays. Similarly for the other months

I'm trying to find out what is the probability that a randomly chosen January will have 5 Sundays. Of course the answer for 4 Sundays would be 1. I presume that 31 day months will have a higher ...
1
vote
1answer
39 views

How to use Wolfram|Alpha to calculate Friday the 13ths

I know someone born on the 13th and we were talking about how Friday the 13th is his birthday from time to time. I thought that might be a good question for Wolfram|Alpha but no matter how I phrase it ...
1
vote
1answer
90 views

Formula to calculate difference between tow dates

I am working on getting date difference I have a formula to calculate it as follows 365*year + year/4 - year/100 + year/400 + date + (153*month+8)/5 but its not ...
1
vote
1answer
35 views

Day of week - 4th June, 2002 using Zeller's Rule

I know how to calculate day of week using Zeller's Rule, but the answer is coming as Sunday, while the correct answer is Tuesday. Where am I doing wrong? Please explain your answer step-by-step. ...
1
vote
0answers
35 views

Why this formula counts passed leap years in Persian arithmetic calendar?

I was reading about a calendar system with these characteristics: Years are grouped into cycles which begin with four normal years after which every fourth subsequent year in the cycle is a leap ...
1
vote
0answers
50 views

Calculating day on date [duplicate]

Possible Duplicate: Calculate which day of the week a date falls in using modular arithmetic Yesterday there was a guy on TV. He asked people in the audience at what date they were born and ...
0
votes
1answer
102 views

A year having more than one Friday the 13th?

We know that every year has at least one Friday the 13th. What about two Friday the 13ths, in a year? What is the probability of a year having two Friday the 13ths? (interesting subquestion here is ...
0
votes
2answers
188 views

What is the minimum number days between one Friday the 13th and the next Friday the 13th?

What is the minimum number days between one Friday the 13th and the next Friday the 13th?(Assume that the year is a leap year)
0
votes
2answers
312 views

Modular Arithmetic Calendars

If a calendar has 427 days in the year and 8 days a week and the first day of their current year, which is 1027 falls on the second day of their week. What day of the week will the first day of the ...
0
votes
1answer
21 views

calendars problem using zellers formulae

i've solved most of the day finding problems using zellers formulae $$ Z= K + \frac{13M -1}{5} + D +\frac{D}{4} + \frac{C}{4} - 2C $$ where $K$ = given $M$ = given month no. ( but here month ...
0
votes
3answers
1k views

How often in years do calendars repeat with the same day-date combinations (Julian calendar)?

E.g. I'm using this formulas for calculating day of week (Julian calendar): \begin{align} a & = \left\lfloor\frac{14 - \text{month}}{12}\right\rfloor\\ y & = \text{year} + 4800 - a \\ m & ...
0
votes
1answer
106 views

How to calculate Anniversary Billing for Uneven time frames?

What is the best way to calculate anniversary billing monthly with different lengths We want to charge for storage say starting June 1st to July 1st and if the customer stays longer than July 1st we ...
-1
votes
1answer
347 views

Math Riddle Involving Birthdays [closed]

So someone asked me the following riddle: If a girl is born in the 19th century, and on her first birthday she is 8. How is this possible? I think it's a simple mathematics problem but I can't find a ...