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'Weekly Challenge 41: Happy birthDay' printed from http://nrich.maths.org/
Zeller worked out a formula to calculate the day of the week for
This formula contains a lots of symbols and terminology, as
In Zeller's formula $d$ stands for the day of the week, numbered
$0$ to $6$ for Saturday - Friday.
$n$ is the day of the month, numbered 1 to 28, 29, 30 or 31
depending on the month in question.
$m$ is the month, numbered from $3-12$ for March - December; $m=13$
in January and $m=14$ in February.
$y$ is the last two digits of the year, or the last two digits of
the previous year if $m=13$ or $14$.
$C$ is the first two digits of the year.
'int[$x$]' is a function which rounds $x$ down to the nearest
integer or returns $x$ if $x$ is already an integer.
'mod 7' means return the remainder when divided by 7.
There are two parts to your task:
1) Check that you can use the formula to work out the day of the
week for a few dates.
2) (Difficult extension) Work out why it is, either roughly or
exactly, that Zeller's algorithm works. A spreadsheet might help to
work out why each term is present in the algorithm.
know ... ?
Date algorithms are complicated by leap years, when there are 29
days in February. Leap years occur roughly every 4 years, although
on occasions a leap year is skipped. The precise rule for
determining leap years is as follows:
If the year modulo 400 is 0 then it is a leap year; else if
the year modulo 100 is 0 then it is not a leap year; else if
the year modulo 4 is 0 then it is a leap year; else it is not
a leap year.
Some human calculators are able to run Zeller's algorithm in their
heads. Can you learn how to do this? You can see an awesome human
calculator in action on You