The Doomsday Algorithm

Usage:

./pi-day-calc.py

Enter a 4 digit year between 1700 & 2099: 2084

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In 2084 pi day (3/14) falls on a Tuesday.
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The Math Involved

The crux of the thing is (ˣ⁄₄ + x) mod 7 - (ˣ⁄₄ + x) mod 1 with adjustments needed for the starting position day of each century. Those repeatedly rotate through [2, 0, 5, 3] with 0 being Sunday.

Example (century starting position day):

2 Tuesday - 1600's
0 Sunday - 1700's
5 Friday - 1800's
3 Wednesday - 1900's
2 Tuesday - 2000's
0 Sunday - 2100's
5 Friday - 2200's
etc...

In Python:

>>> x=91
>>> # (x/4+x)%7-(x/4+x)%1
>>> # simplified version (because `int` takes care of the extra digits left over from the float):
>>> int(x/4+x)%7

1

In Excel:

So for 1991 (91) it would return "1". Add that to it's century start day of Wednesday(3) and you'd get "4".

0 Sunday
1 Monday
2 Tuesday
3 Wednesday
4 Thursday
5 Friday
6 Saturday

3/14/1991 was on a Thursday!

- sb :)