# 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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### 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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### 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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### 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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### 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 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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### 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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### 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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### 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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### 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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### 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 ...
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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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### 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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### 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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### 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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### 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 ...
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### 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?
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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 ...
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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 ...
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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 ...
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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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### 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 ...
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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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### 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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### 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?
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### 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?
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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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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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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### 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 ...
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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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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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### 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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### 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?
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 ...