Questions tagged [calendar-computations]

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.

Calendar computations have a long history within mathematics. In fact, much of ancient mathematics (such as those developed by the Babylonians, Mayans, and Chinese) stem from an effort to try to understand the mathematical relationships (especially the quasi-periodic nature) between the solar year, the lunar month, and the sidereal day.

With the development of the Gregorian calendar, in modernity the academic interest in calendar computations have somewhat waned. But there are still many interesting recreational problems related to the computations of dates, the interaction between lunar and solar calendars, and relationship between the human concept of the week with more astronomically based measurements of time.

131 questions
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Can there be a month with 6 Mondays? (or 6 of any other days?)

This year, this month (November) we've 5 Mondays so I get 5 pay checks on 2nd, 9th, 15th, 22nd, 29th (which feels very good - I get paid one extra check :-). I wonder if it's possible some years to have 6 Mondays? I haven't seen it but I wonder if…
bodacydo
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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 sequence of these pairs. For example, starting from…
Truong
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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 year. Cycles are grouped into grand cycles of either…
reith
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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 Date have been set up, but to make it simple,…
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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 does it fluctuate? If it fluctuates, is there a…
Steven Lu
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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 years : 1600 years = 24 x 16 = 384 leap years (100…
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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 one, any ideas?
Quixotic
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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 angle between the sun and moon. Now I have many…
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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. Thanks. :) /**** EDIT ****/ All right. I got the right…
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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 ?
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Prove That the Shortest Period of the Gregorian Calendar is 400 Years

I ask for help. I would like to resolve the following question: Let $A$ be the set of natural numbers greater than 1582. If, for every $Y\in A$ , the years $Y$ and $Y + n$ (of the actual calendar, the Gregorian) have the same calendar, then $n =…
Paulo Argolo
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A question about leap year

Very difficult to me, It is a question about leap years: "In the western calendar, a year having 365 days is called a common year, while a year having 366 days (with an extra day, February 29) is called a leap year. People always say that when a…
user256670
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probability that a number is a leap year

I have been asked the following question in an exam in Mathematics Phd Programme as a level of IQ Test. However I don't know how to figure it out. November 9,1994 was a Wednesday. Then what day will be November 9,1965 and November 9,1970? One way…
Learnmore
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Get number of week by given date and day of week

Is there a formula to get the number of week by a given date and day of week for example Oct 15, 2014 wed. how do i get what number of week is it?
user206250
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Make a calendar such that the number of days between two specified days is the least value

The last monday of a 31-day month must be at least how many days after the first Friday of the same month? I have a question about the two methods to solve the problem I don't understand the intuition behind the two methods. Can I get a drawing to…
user159778
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