Doomsday rule

About the task

John Conway (1937-2020), was a mathemetician who also invented several mathematically oriented computer pastimes, such as the famous Game of Life cellular automaton program. Dr. Conway invented a simple algorithm for finding the day of the week, given any date. The algorithm was based opon calculating the distance of a given date from certain "anchor days" which follow a pattern for the day of the week upon which they fall.

Algorithm

The formula is calculated assuming that Sunday is 0, Monday 1, and so forth with Saturday 7, and

   anchorday = (Tuesday(or 2) + 5(y mod 4) + 4(y mod 100) + 6(y mod 400)) % 7

which, for 2021, is 0 (Sunday).

To calculate the day of the week, we then count days from a close doomsday, with these as charted here by month, then add the doomsday for the year, then get the remainder after divding by 7. This should give us the number corresponding to the day of the week for that date.

   Month	        Doomsday Dates for Month
   --------------------------------------------
   January (common years)   3, 10, 17, 24, 31
   January (leap years)     4, 11, 18, 25
   February (common years)  7, 14, 21, 28
   February (leap years)    1, 8, 15, 22, 29
   March	             7, 14, 21, 28
   April	             4, 11, 18, 25
   May	                     2, 9, 16, 23, 30
   June	             6, 13, 20, 27
   July	             4, 11, 18, 25
   August	             1, 8, 15, 22, 29
   September	             5, 12, 19, 26
   October	             3, 10, 17, 24, 31
   November	             7, 14, 21, 28
   December	             5, 12, 19, 26

Task

Given the following dates:

1800-01-06 (January 6, 1800) 1875-03-29 (March 29, 1875) 1915-12-07 (December 7, 1915) 1970-12-23 (December 23, 1970) 2043-05-14 (May 14, 2043) 2077-02-12 (February 12, 2077) 2101-04-02 (April 2, 2101)

Use Conway's Doomsday rule to calculate the day of the week for each date.

see also