Day and Date Calculations — Fundamental Concepts

Fundamental Concepts

The weekday repeats after seven elapsed days. Reduce any day difference to its remainder on division by seven, then move forward or backward from the known weekday. A common year has remainder one and a leap year remainder two, but a matching-date interval gains the extra day only if it actually crosses 29 February.

Use the Gregorian leap-year test in stages: divisible by four; century years excluded unless divisible by four hundred. Thus 2000 is a leap year, while 1900 and 2100 are not. February has 29 days in a leap year and 28 otherwise. Historical civil-calendar questions can require an explicit calendar assumption because adoption dates differed between jurisdictions.

For an original worked premise, if 1 January 2024 is Monday, then 1 March lies 31 + 29 = 60 days later. The remainder four gives Friday. If 10 April is Thursday, 5 May is 25 days later and therefore Monday. Count the interval to the next month carefully rather than including both endpoints as elapsed days.

Backward questions use the same arithmetic with the opposite direction. If 20 June is Saturday, 5 June is fifteen days earlier, giving Friday. A 400-year Gregorian cycle has 97 leap years and a total divisible by seven; the simpler 28-year shortcut is interrupted by century exceptions.