Zeller's Congruence

Zeller’s Congruence is a modular arithmetic shortcut that turns a calendar date into a weekday number by counting how many days the date is offset from a fixed pattern of 7-day cycles. The month is re-encoded so that March starts the year, which makes leap-day handling much cleaner because February is treated as the last month of the year. The extra floor terms account for the extra day every 4 years, while the century terms correct for the fact that Gregorian leap years are skipped on most century years unless divisible by 400.

Use it when you need the weekday for a Gregorian date without consulting a calendar, especially in programming, puzzle solving, historical date checks, or manual verification. It is most useful for dates after the Gregorian reform and for tasks where exact weekday computation matters.

• Using the ordinary month number for January and February instead of treating them as months 13 and 14 of the previous year
• Forgetting to split the year into K and J correctly, which changes the century adjustment terms
• Misreading the output mapping for h, since 0 corresponds to Saturday rather than Sunday