Calendar
Calendar
Calendar problems involve finding the day of the week for a given date, identifying leap years, or determining when two years share the same calendar. The core technique is counting 'odd days' — the extra days beyond complete weeks in a given period.
Key Idea
Count odd days for the entire period, take mod 7, map to day name. Memorise odd days for 100/200/300/400 year periods — they're always the same.
Core Formulas
Ordinary year odd days
365 days = 52 weeks + 1 odd day
Counting extra days in an ordinary year
Leap year odd days
366 days = 52 weeks + 2 odd days
Counting extra days in a leap year
Century odd days
100 yrs=5, 200 yrs=3, 300 yrs=1, 400 yrs=0 odd days
Pre-computed odd days for century multiples
Day number mapping
0=Sun, 1=Mon, 2=Tue, 3=Wed, 4=Thu, 5=Fri, 6=Sat
Converting odd day total to weekday
Leap year rule
Divisible by 4 (not century) OR divisible by 400 (century)
Determining if year is a leap year
Relevant Exams
1–2 questions per exam. Most common: find day of week for a given date, identify leap year, or find which years have same calendar. Quick to solve with odd days method.