# Tagged Questions

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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### 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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### Why isn't 1900 a leap year? [closed]

I searched leap years online and found that 1900 is not, contrary to what I thought, a leap year. But, why is it not if 1900 is divisible by 4: $\frac{1900}{4} = 475$ My brother was working on his ...
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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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### Why is it that if I count years from 2011 to 2014 as intervals I get 3 years, but if I count each year separately I get 4 years?

I'm not a very smart man. I'm trying to count how many years I've been working at my new job. I started in May 2011. If I count the years separately, I get that I've worked 4 years - 2011 (year 1), ...
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### How can one manually calculate the date conversion to the Hebrew calendar

There already are algorithms that can be used to concert a date from different calendars into the Julian Day Number (JDN) and a JDN into the Hebrew calendar. But how can one calculate the conversion ...
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### 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 ...
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### 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 ...
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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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### Is it possible to have such date and day combination that doesn't occur on any year ever?

My friend told me a story yesterday and said "It happened on March 13th and it was Friday". I was thinking about this and I've a question. Is it possible to have such date and day combination that it ...
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### perpetual calendar on five dice

Does anyone know how to create a perpetual calendar on the sides of five dice ? The calendar is required to show just two digit day, and three letter month name. Apparently this can be done using ...
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### how to determine particular months with five weekends

January of 2016 has five Fridays, five Saturdays and five Sundays. What is the next January that will again have five weekends like this?
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### how to determine the day of the week when some clues are given?

In a year, there are more Mondays than Fridays, and more Sundays than Wednesdays. Which day of the week is the first day in March of that year?
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### Friday the 13th future possible

A year normally has at most three Fridays the 13th. Year 2015 has three such days. What is the next year that has three Fridays the 13th again for the first time?
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### Months and notes. Pure coincidence? [closed]

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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### Which day of the week will be $100$ days from now

If today is Wednesday, what day of the week will it be $100$ days from now? Going forward $1,8,15,\dots,92,99$ days all result in Wednesday. So the $100$th day will be Thursday. But the solution ...
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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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### What adjustments would be necessary to have a remainder of 0 associated with Sunday?

I was reading this below and I had a question: http://mathforum.org/dr.math/faq/faq.calendar.html Take a look under "The Key Value Method" where it says "A remainder of 0 corresponds to Saturday, 1 ...
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### Why do you subtract 1 in a leap year if the date falls before March?

I was reading this below and I had a question: http://mathforum.org/dr.math/faq/faq.calendar.html Take a look under "The Key Value Method" where it says "If your date is in January or February of a ...
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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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### Probability that a year contains 53 Mondays

The question: Find a probability that a year chosen at random has 53 Mondays. Now I know in a non-leap year, probability of getting 53 Mondays is $\frac{1}{7}$ and in a leap year, probability of ...
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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 ...
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### Calculate day from x position, when some spacer elements are used

Look at the following sketch: This should be a calendar view. In the beginning and the end of each week a 2 px separator is used (blue line). A week consists of seven days. Each day has a certain ...
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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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### 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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### Calculate the distance between days of the week

I'm trying to create a formula that will give me the distance in days between 2 different days of the week with min/max of +7/-7. So for instance is there a formula to find that the days between this ...
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The problem is here and someone gave this answer but I don't understand it even if I know the rule of large numbers. If you want to write a code for this, it is really boring. On the other hand, ...
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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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### 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. ...
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### 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 ...
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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 ...
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### 4-4-5 retail calendar - calculating extra week

I have been tasked with making a 4-4-5 calendar for a retail reporting system (in javascript using moment.js but this shouldn't matter). http://en.wikipedia.org/wiki/4-4-5_calendar A 52 week year is ...
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### Proof about Friday the 13th

Few years ago I learned that there are more friday the 13th in the 400 years period of our calendar, than all other days, but I have never found any proof ! Can you help me please ?
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### Is Christmas equally Likely to fall on any day of the week? [duplicate]

Assuming Christmas day falls on the 25th of December every year, and using the Gregorian calendar, is it equally likely to fall on any day of the week? (With no prior knowledge about last year's ...
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### Calculate difference in days to reference date

This question is related to a programming question. Because I think it's pure mathematic I post this question here. I want to calculate the difference in days to a reference point. Therefore I have ...
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### Question about Gauss' Determination of the first day of the year.

On the wikipedia article http://en.wikipedia.org/wiki/Determination_of_the_day_of_the_week#Gauss.27_algorithm it explains the Gaussian Formula for calculating the first day of the year. I was ...
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### Converting decimal dates to calendar dates?

I have the decimal number 2005.067 which represents the date January 25, 2005. The math equation below shows how the decimal number is created 2005 + (25 - 0.5)/365. I want to be able to grab 2005.067 ...
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### when to use ( end point/date - start point/date + 1) , and when to use end point /date - start point /date? [duplicate]

This is a simple question on difference. I have seen the following situation - for example how many day you spend on a travel when the travel date was 14-Aug-2014 till 25-August-2014. The answer for ...
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### Probability of a year which is not a leap year

If a 4 digit year is choosen randomly, what is the probability that it is not a leap year ? This problem has come in my exam and i have written like this I know that the number of four digit year ...
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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 to find the date for the recurring events in calendar?

In my scenario, I have a event (e1) with ...
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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?
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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 ...
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### 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 ...
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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?
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### 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!
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### 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 ...
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### 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 ...
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### 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 ...
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 ...