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Laziness had taken us down a slightly errant path. Rather than adding 5, 10, 15, 20, 25, 30, 35, 40, ..., we're subtracting 2, 4, 6, 8, 10, 12, 14, 16, ..., for the years 1904, 1908, 1912, 1916, 1920, 1924, 1928, 1932, .... Every time we use this second method for the years between the years already mentioned, we're always wrong by 6, 4 and 3. That is, for 1900, the error is 0; the calculation is right on the mark. For 1901, the calculation is off by 6; for 1902, the calculation is off by 4; for 1903, the calculation is off by 3. Then for 1904, the calculation is totally correct. Thus we have a repeated error of 0, 6, 4, 3, 0, 6, 4, 3, 0, 6, 4, 3, ..., for the years 1900, 1901, 1902, 1903, 1904, 1905, 1906, 1907, 1908, 1909, 1910, 1911, .... Notice that an error of 6 is the same thing as an error of -1; an error of 4 is the same thing as an error of -3; and an error of 3 is the same thing as an error of -4. So we can repeat this same error pattern as follows: 0, -1, -3, -4, 0, -1, -3, -4, 0, -1, -3, -4, ..., for the years 1900, 1901, 1902, 1903, 1904, 1905, 1906, 1907, 1908, 1909, 1910, 1911, .... So here's the final year adjustment: Take the last two digits of the year; divide by 2, dropping any remainder; if that result is odd, subtract 3; if the original year is odd, subtract 1. Count UP to the nearest multiple of 7, and that's it. That sequence will correct any errors, don't ask me why. It just does. |
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Of course, we still have to account for differences between centuries. From 1900 to 1999, including the leap day snatched backwards from 2000, we have (365+365+365+366 days) x (25 4-year sequences in a century) = 36525 days in the 20th century. 36526 is evenly divisible by 7, so we're one short of the mark. From 2000 to 2099, including no leap day snatched backwards from 2100, because that centesimal year is a common year, we have (365+365+365+366 days) x (25 4-year sequences in a century) - 1 = 36524 days in the 21st century, which is two short of the mark. Factoring this information into the year adjustment, we have: Take the last two digits of the year; divide by 2, dropping any remainder; if that result is odd, subtract 3; if the original year is odd, subtract 1. If in the 1900's do nothing; otherwise, if beyond 2000, or 2400, add 1 for each of them; add or subtract 2 for other centuries; Count UP to the nearest multiple of 7, and that's it. |
8:59 |
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This whole time we've been sneakily using March 25th as New Year's Day, in order to get any leap day, February 29, hanging off the back of the previous year, rather than throwing off the grid in any actual leap year. In order to get New Year's Day back where it belongs, at January 1st, we'll use two different month codes for January and February. If we're in a common year, the month codes for January and February are "x" = 1, and "xfeb" = 4. If we're in an actual leap year, such as 1904, 1908, ..., 1996, 2000, 2004, ..., the month codes for January and February are «none» = 0, and "feb" = 3. This is equivalent to the Floor Manager locking up the store at the end of the day, then going back in to lock up the cash box, then going back in to turn on the night display lights. |
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(1) 47 / 2 = 23 |
(1) 52 / 2 = 26 |
(1) 32 / 2 = 16 |
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(2) 23 - 3 = 20 |
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(3) 20 - 1 = 19 |
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(4) 16 + 1 = 17 |
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(5) 19 up to 21 = 2 |
(5) 26 up to 28 = 2 |
(5) 17 up to 21 = 4 |
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(7) 37 down to 35 = 2 |
(7) 29 down to 28 = 1 |
(7) 5 down to 0 = 5 |
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2 = Monday |
1 = Sunday |
5 = Thursday |
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Good days for a picnic. |
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