What months have 5 working weeks?

Answer 1

IF THE NUMBER OF 'WEEKS' in a month is determined by how many weekly pay days fall in a particular month, then, in a leap year, and subject to a maximum of 5, each month has the potential of being a '5 week' month.

In non-leap-years, and again subject subject to a maximum of five, each month except February has the potential of being a 5 week month,

BUT IF A WEEK is defined as a 'working week', and the 'working week' is a period of five consecutive days followed by two rest days, there are no months which have or can have five working weeks.

This can be proven as follows:

1. A working week has 5 days.
2. Five working weeks is 25 days (5 x 5).
3. The working weeks are separated from each other by 2 'non-work' days.
4. Between five working weeks there are 4 periods of 2 'non-work' days, i.e. 8 days (4 x 2)
5. To achieve five working weeks you need 25 work days plus 8 non-work days in between.
6. The minimum total of days required for 5 working weeks is therefore 25 + 8, which is 33 days.
7. The longest month has only 31 days, which is 2 days short of the minimum number of days required for 5 working weeks.
8. Therefore the maximum period of working weeks in the longest months of the year are four and three fifths working weeks.

Of course, if a working week is only 3 consecutive days, then every month with 31 days and that starts on a working day will have 5 working weeks:

1. Five working weeks is 15 days (5 x 3)
2. The working weeks are separated from each other by 4 'non-work' days.
3. Between five working weeks there are 4 periods of 4 'non-work' days, i.e. 16 days (4 x 4)
4. To achieve five working weeks you need 15 work days plus 16 non-work days in between.
5. The minimum total of days required for five 3-day working weeks is therefore 15 + 16, which is 31 days. No problem!

If a person's 'working week' in a particular situation is only two consecutive days long, in months with 31 days the maximum number of working weeks is still only five.

This is because, although the pattern of 2 working + 5 non-work days requires only 30 days for a period of five '2-working day' weeks, the remaining day has to be a non-work day at one end or the other of the month.