====== what year might that have been? ======


> Given an invitation for an event on "Saturday, April 26th," for instance, might it (if correct, of course) have been from last year? 

Without consulting a perpetual calendar((phone books and almanacs used to have those, but I don't know where I'd look for one today without using a search engine on the Internet)), here's one solution that uses a sort of back of the envelope perpetual calendar that is easy to construct.

===== The Principle of the Method =====

The idea is to figure out what day of the week January 1 had to fall in order for your date to fall on the right day of the week; for dates after February, two weekdays will be possible, one for leap years and one for other years. Then, figure out which years started that way; that is easy to do from the calendar of the current year (or a good memory).

  - calculate how many days came before your date (including January 1).
  - calculate the remainder modulo 7 to get the weekday difference between January 1 and your date.
  - build the table of January 1 weekdays.
  - look up the possibilities.

===== Date Serial Number =====

The serial number for a date can be computed as the sum of month lengths of prior months in the year plus date minus 1.

==== Example ====

^ Month  ^ Non-leap ^ Leap ^
| January (all)  |  31|  31|
| February (all) |  28|  29|
| March (all)   |  31|  31|
^ s/total  |  90|  91|
| April (date)   |  26|  26|
^ total    |  116|  117|
^ minus 1 (total prior days) |  115|  116|
^ modulo 7   |  3|   4|

What this means is that April 26 falls some number of weeks plus either 3 or 4 days after January 1. Thus, if April 26th were a Saturday, January 1 must have been either a Wednesday (non leap year, 3 days before Saturday) or a Tuesday (leap year, 4 days before Saturday).

To compute "modulo 7" just divide by seven and keep the remainder: 115 = (7 * 16) + __3__ .
===== Mini Perpetual Calendar =====

Now we need to know what weekday January 1 fell (or will fall) in each year!  Here's a table with the answers, but it is pretty easy to reconstruct if you don't have it at hand. 

  * The year after a leap year starts two weekdays later than the leap year did, 
  * otherwise a year starts one weekday later than the previous year did.
  * It repeats after 28 years (7 rows).

So starting with Sunday in 2012, we can easily construct this table:

^  When  ^  Year  ^  Year+1  ^  Year+2  ^  Year+3  ^
^ 2012  |  Sun  |  Tue  |  Wed  |  Thu  |
^ 2008  |  Tue  |  Thu  |  Fri  |  Sat  |
^ 2004  |  Thu  |  Sat  |  Sun  |  Mon  |
^ 2000  |  Sat  |  Mon  |  Tue  |  Wed  |
^ 1996  |  Mon  |  Wed  |  Thu  |  Fri  |
^ 1992  |  Wed  |  Fri  |  Sat  |  Sun  |
^ 1988  |  Fri  |  Sun  |  Mon  |  Tue  |

Done!

==== Example (continued) ====

When has there been Saturday, April 26? When have there been leap years starting on Tuesday or other years starting on Wednesday?

^  When  ^  Year  ^  Year+1  ^  Year+2  ^  Year+3  ^
^ 2012  |  Sun  |  Tue  |  __Wed__  |  Thu  |
^ 2008  |  __Tue__  |  Thu  |  Fri  |  Sat  |
^ 2004  |  Thu  |  Sat  |  Sun  |  Mon  |
^ 2000  |  Sat  |  Mon  |  Tue  |  __Wed__  |
^ 1996  |  Mon  |  __Wed__  |  Thu  |  Fri  |
^ 1992  |  Wed  |  Fri  |  Sat  |  Sun  |
^ 1988  |  Fri  |  Sun  |  Mon  |  Tue  |

  * Answer: 2008, 2003, 1997,
  * Also 28, 56, 84 (etc.) years prior: 1980, 1975, 1969, 1952, 1947, 1941 (etc.)