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.

138 questions
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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? Source: 2010 ISI B Math UGB
33
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3 answers

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 wondering how to find instead the expected number of…
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Decoding Gauss' Easter Algorithm

In 1800, Gauss published this algorithm for computing the date of Easter in a given year $year$: $a = year \mod 19$ $b = year \mod 4$ $c = year \mod 7$ $k = \lfloor year/100 \rfloor$ $p = \lfloor (13 + 8k)/25 \rfloor$ $q = \lfloor k/4 \rfloor$ $M…
user139000
28
votes
3 answers

Why does this age calculation trick work?

The trick works like this: Take the current date in the format yyyymmdd and subtract it with your date of birth taken in the same format. Drop the last four digits to get your age. For example, I was born in August 20th, 1994. Today it is July 13th,…
user41235
  • 734
18
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4 answers

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 to do it. Can someone point me to the right…
16
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2 answers

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 Saturday. However, due to 2012 being a leap year, my…
Spudley
  • 275
13
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3 answers

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, 17, and 19 -- are leap years. Someone reduced…
Dave
  • 133
13
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Months and notes. Pure coincidence?

There are $12$ months in a year and $12$ notes in the chromatic scale. Moreover, there are $7$ long and $5$ short months and there are $7$ white and $5$ black keys in each octave on the piano keyboard. The patterns of long/short months and…
12
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4 answers

Smallest future date which involves no repetition of a digit in the format DD/MM/YYYY

What is the smallest future date which involves no repetition of a digit in the format DD/MM/YYYY for the year? What is your approach?
9
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1 answer

Formula to find the day of any date in Gregorian calendar derivation.

My teacher taught an expression to find the day of any date in the Gregorian calendar. Expression: $$ \bbox[5px,border:2px solid red] { D\equiv {d+c_m+c_y+c+\left\lfloor\dfrac c4\right\rfloor \pmod7} } $$ Where $D$ is the day code of the given date…
Wolgwang
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Under the Gregorian calendar, what days can never be Easter?

Obviously, October 31 can't be Easter any year whatsoever. Indeed no day in October can be Easter. But can February 28 be Easter? What about February 29? May 1? Is there a single consecutive range of days that can't be Easter, like say for example…
Robert Soupe
  • 14,999
7
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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. Temporarily (for the duration of this question) assume for…
7
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5 answers

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 & = \text{month} + 12a -…
5
votes
4 answers

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?
basarat
  • 165
5
votes
4 answers

Why don't we subtract out / ignore the leap year every 128 years?

When we add the extra day to the calendar every 4 years it's to "correct" the calendar under the assumption that the year's length is 365.25 days. Every year, you're .25 days off, so after 4 years, you're 1 day too far ahead, so add in an extra day…
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