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Why 2011 will be a day-by-day repeat of 2005

Dec. 30: Those of you who married in 2005 can flatter your spouses next year by remembering not only the wedding date but also the day of the week it happened.

If you are wondering how, it’s very simple. All the dates in 2011 and 2005 fall on the same day of the week. So if you had married on a Wednesday, your anniversary will be a Wednesday, too, and you can point out the “coincidence” and buy a special present to score brownie points.

Coincidence? Not a chance. It’s simple arithmetic. Years with the same date-day correspondence — let’s call them analogous years or ana-years for convenience — repeat according to a pattern.

This is how. If every year had 364 days, then all years would be ana-years because 364 is exactly divisible by seven (the number of days in a week). But since each year, leaving out leap years, has 365 days, you have to advance the day by one.

For example, since December 31 in 2010 is a Friday, December 31 in 2011 would be a Friday plus one day — a Saturday. Do this seven times, and you get back to Friday. So, if every year had 365 days, ana-years would repeat after every seven years.

But since there was one leap year, 2008, between 2005 and 2011, we have to add one more extra day, because a leap year has 366 days. Therefore, 2005 has an ana-year after a gap of six, not seven years.

But don’t expect every year to have an ana-year after six years, for often there are two leap years in between. For instance, working backwards, there were the leap years 2000 and 1996 between 2005 and 1999, which means the last two are not ana-years.

So what’s the previous ana-year for 2005? It was 11 years ago, 1994. Here’s why: Between 1994 and 2005 there were three leap years: 1996, 2000 and 2004. The 11-year gap means you have to add 11 extra days for each year and a further three days for each leap year. That gives you 14, which is divisible by seven.

After 2011, the next ana-year will come not six years but 11 years later, in 2022. (See chart)

So, is it always either a six-year gap or an 11-year one between ana-years? Yes, with an 11-11-6-11-11-6 pattern, but there are exceptions that we’ll discuss in a minute. But some good news first.

Sometimes the combination of sixes and elevens yields 50, so the golden anniversary for some of you will fall on the day of the week you had married.

Example: 1955 and 2005, whose ana-year pattern goes like this: 1955, 1966, 1977, 1983, 1994, 2005. Those who marry in 2011 too will be lucky in 2061.

What about 51 years? If you are wondering why 51, here’s the reason. The first cricket Test that India played began on June 25, 1932, at Lord’s. By coincidence, India won its only World Cup too on June 25 — in 1983 at Lord’s again — making the date a red-letter day for Indian cricket.

However, not by coincidence but by the inexorable rules of arithmetic, both days were Saturdays, too.

But does that mean 1932 and 1983 were ana-years? They couldn’t be, because one is a leap year and the other is not. It’s just that even outside ana-years, you can have a date-day correspondence over parts of two different years if one is a leap year and the other is not. Either the days from January 1 to February 28 tally, before the extra February 29 ends the correspondence, or the days from March 1 till December 31.

So, although six years is the shortest gap possible between ana-years, it can be five years for a simple date-day match. Example: the dates from March 1 till December 31 for the years 2003 and 2008.

Now, the exceptions. Leap years must wait for 28 years to have an ana-year (which, obviously, must be a leap year too), so don’t ever marry on February 29.

But even here there are exceptions. Years like 2100, 1900, 1800 or 1700 — which end a century (or begin it, depending on how you count) — are not leap years unless they are divisible by 400, like the year 2000 was.

Their occurrence skews calculations and can spring ana-years separated by not six or 11 years but 12 years (as the 2097-2109 and 2098-2010 pairings will be). Plus, it also breaks the 28-year rule for leap years. So, 2096 will have an ana-year in 2008 — a gap of 12 again.

But the biggest surprise will be for those who marry on any date on or after March 1 in 2096. They’ll have a date-day correspondence in 2103, exactly seven years after they married.

Just think how great it will be to give your spouse the special anniversary gift just when the “seven-year itch” has been looming.

Don’t put off your wedding till 2096, though. Marry now and bequeath that good fortune to your great-grandchildren.

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