February 2004 - leap year

Considering each year is technically 365 days and about 6 hours, we are actually gaining on some deferred interest on loans and losing on deferred interest on savings as we only pay/receive every 4 years.

In message , Dudley writes

What do you do when there are a different number of sundays in one year than for another

But not those on annual interest calcs.

Not personal loans of the old 'flat rate added at the beginning type'

Err ...

All of which would be fine if it weren't for the fact that three century years in four are not leap years ... and by a curious coincidence (well, 1 in 7 chance) 366*97 + 365*303 = 146097, which *is* divisible by 7, hence the cycle lasts for only 400 years and not the 2800 you might expect, and there are 7 possible sequences of which only 1 actually happens (until the next calendar reform at least).

And the other thing to note is that 4800 (the number of months in 400 years) is not divisible by 7, which must mean that some dates are more likely to fall on certain days than others. A reasonably simple basic program should be able to work out what the chances of the 13th being a Friday are....

In message , Andy Pandy writes

Bur as the number of days in a month can have four different answers, why is your deduction such a surprise?

Over what period?

A period of 400 years (not spanning a calendar reform) starting on *any* date, will contain 146097 days, as Stephen said, which is exactly 20871 weeks.

Therefore each weekday will occur exactly 20871 times, but that says nothing about the distributions specific to any particular date. If you do a full count, it turns out that the 13th will fall on a Friday 688 times, a Sunday and Wednesday 687 times, a Monday and Tuesday 685 times, and a Saturday and Thursday 684 times.

Curiously, for each date in the range 1 to 28, no weekday ever occurs 686 times, and inded each date distributes in a rotating sequence of 680 + (8, 4, 7, 5, 5, 7, 4) times. In other words, Thursday the 12th is exactly as frequent as Friday the 13th, as is Saturday the 14th, etc.

as is Saturday the 14th, etc.

Thinking about that ... really quite logical!

It's got nothing to do with different numbers of days in the months. As per Tim's post, if it wasn't for the century leap year rule, every date would be equally likely to be on any particular day.

From the big bang until Scotland win the world cup. Using today's calendar rules.

2) ISTM that all that happens is that it shifts the starting day by one, every 4ths set of 28 years and you have to start counting again.

um, OK then, this was all just a bit too much to consider in my spare moments.

Tim

So if you can find a calendar for 1603 you can use it this year - but not if it was English since we didn't adopt the Gregorian calendar until 1752 ...