Ok, I think the OP means 4 weeks as in 4 lines and no partial lines on a printed calendar unlike the 2014 one above which has 5 printed (some partial) lines. The term the OP was missing in the post is "perfect month"
Thus you must start, using the traditional American way of presenting a calendar, with Feb 1st being a Sunday for this year to be a perfect month. As there are 7 days in a week, one of every seven years would seem to have Feb 1 be a Sunday. If there were no leap years, then the correct answer would be, 1 in 7 years the Feb calendar consists of just 4 lines. However we have leap year. Every leap year fails as they obviously have 29 days. And you need to do a correction not just because every 4th year automatically fails but the leap year makes the next year's assignment of Feb 1 advance by one day.
In a normal pair of years which day of the week a particular date falls upon goes up by one. Thus in 2013 Feb 1 was a Fri, in 2014 it was a Sat and in 2015 it is a Sun, in 2016 it will be a Mon even though 2016 is a leap year we don't get the leap day until after Feb 1. Then in 2017 it will be a Wed. 2018 a Thurs, 2019 a Fri, 2020 a Sat. Here is gets interesting as 2021 it should be a Sunday again creating a perfect month but NO, it is a Mon as we have a leap day in 2020. The next perfect month will be .. c'mon draw it out for yourself now that you see the pattern (every 6 or 11 years by the way)
|