Calendars Quiz

2007 is an ordinary year, which has 1 odd day. Monday + 1 Day = Tuesday.

1900 is a century year. For it to be a leap year, it must be divisible by 400. Since 1900/400 is not zero, it's not a leap year.

$64 / 7 = 9$ weeks + 1 Odd Day. Tuesday + 1 = Wednesday.

100 years have 5 odd days. So, 200 years have $5 \times 2 = 10$ days. $10 / 7 = 3$ remainder. Result: 3 odd days.

From Aug 15 1947 to Jan 26 1950: days = 138 (1947) + 366 (1948) + 365 (1949) + 26 = 895. $895 mod 7 = 6$. Friday + 6 = Thursday.

2028 is a leap year (366 days) = 52 weeks + 2 odd days. Jan 3 is Monday. Over 52 weeks there are 52 Mondays, plus Jan 3 adds an extra Monday. Total = 53 Mondays.

2000 to 2099 = 100 years containing 24 leap years (2000, 2004, ..., 2096) and 76 ordinary years. Odd days = $24×2 + 76×1 = 124 ≡ 5$ (since 2000 is a leap year). Saturday + 5 = Thursday.

Non-leap year = 365 days = 52 weeks + 1 odd day. 1st day = Wednesday → last day = Wednesday. Sundays occur every 7 days. From Jan 1 (Wed) to first Sunday = 4 days. $52$ full weeks = 52 Sundays. The extra day (Wed) is not Sunday. So only 52 Sundays.

2016 to 2026 = 10 years. Leap years in between: 2016, 2020, 2024 = 3. Odd days = $10 + 3 = 13 ≡ 6$. Monday + 6 = Sunday.

In 400 years, there are 97 leap years and 303 ordinary years. Odd days = $97×2 + 303×1 = 194 + 303 = 497$. $497 mod 7 = 0$. So 0 odd days in 400 years.

$2021 mod 7 = 2021 - 7×288 = 5$. Tuesday + 5 = Sunday.