Calendar Practice Questions

Count the odd days: from 18 Feb 2005 to 18 Feb 2007: 2 year(s), of which 0 contain 29 Feb → odd days = 2×1 + 0×2 = 2. Total odd days = 2 mod 7 = 2. Since we go forward in time, move 2 day(s) forward from Friday → Sunday.

Arun goes only on Thursdays, so the day nine days ago was Thursday. 9 days = 1 week + 2 days → today = Thursday + 2 = Saturday.

2007 is an ordinary year. Add odd days year by year until the total is a multiple of 7 AND the next year is also an ordinary year: 2007: 1, 2008: 2, 2009: 1, 2010: 1, 2011: 1, 2012: 2, 2013: 1, 2014: 1, 2015: 1, 2016: 2, 2017: 1 → total 14 = 2×7, i.e. 0 odd days. So 2018 starts on the same day as 2007 and has the same number of days → same calendar.

A year has 366 days only if it is a leap year. A century year is a leap year only when divisible by 400. 1600 ÷ 400 = 4, so 1600 is a leap year; 1800, 1900 and 2100 are not divisible by 400.

A leap year has 366 days = 52 weeks + 2 days, so it has 2 odd days.