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.
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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
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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 ...
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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 =...
user139000
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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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Smallest future date which involves no repetition of a digit in the format DD/MM/YYYY [closed]
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?
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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}
}...
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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 ...
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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.
...
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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 & ...
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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 ...
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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?
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