In Summary

  • It turns out that 2017 will be identical to 2045, and 2073. This 28-year sequence works fine for any year up to 2099. After that, it breaks down again. 2017, 2045 and 2073 are identical, but 2101 does not fit that pattern. It starts and ends on Saturday, not Sundays.
  • A new sequence begins at the beginning of the 22nd century; thus 2129 will be identical to 2101 … all the way up to 2185. The reason for the pattern breakdown is that 2100 will not be a leap year, even though it is divisable by 4.

A friend sent me this interesting message: “If you have the 2006 or 1995 calendar, don’t buy the one for 2017. They are identical.” So I checked my mobile phone and found that it’s true: those three years start and end on Sundays.

It is not totally unexpected. A week has seven days and a regular year has 365 days; that is 52 weeks and one day.

So, if there were no leap years, the start day of the calendar would progress by one day each year. That is, if one year started on a Monday, the next would start on a Tuesday, and so on. The calendar would repeat itself every seven years. Unfortunately, the leap year breaks the sequence.

Now, since seven (years of the simple sequence) + 4 (years of the leap cycle) = 11, we might expect the calendar to repeat itself after every 11 years. And it is not a wonder that 2017 – 2006 = 11 and 2006 – 11 = 1995. So far the pattern works fine.

However, further extrapolation to 1984 and 2028 does not work: these two years are not identical to 2017. A better pattern emerges when we multiply 7 by 4 instead of adding them. In that case, the cycle is 28 years.

It turns out that 2017 will be identical to 2045, and 2073. This 28-year sequence works fine for any year up to 2099. After that, it breaks down again. 2017, 2045 and 2073 are identical, but 2101 does not fit that pattern. It starts and ends on Saturday, not Sundays.

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