Richard Mallett wrote: >Just to clarify : The answer to the original question is that this >situation recurs every 28 years, so will have occurred in 1987, 1959, >1931, 1903 and 1874 (29 years because 1900 was not a leap year) and will >occur again in 2043, 2071, 2099 and 2128 (29 years because 2100 will not >be a leap year)
Although the situation does usually recur every 28 years, I do not think this is the complete answer, nor that it will occur in 2128, as that is a leap year - when March 13 will fall on Saturday. We would guess that February 13th must be a Friday about one year in seven, or there would not be enough days of the week to go round; and that about one-quarter of these will be a leap year and March 13th will be Saturday. So: Three times in a 28 year cycle (an ordinary one, not including a century non-leap year) February 13 falls on Friday and the year is not leap, so March 13 is also Friday. The intervals are 6, 11, and 11 years, according to whether the start year is 1, 2, or 3 after a leap year, so that they include 1, 3, or 3 leap years. This works because 6+1 and 11+3 are both multiples of 7. The Friday 13th pair in February and March occurred in 1953, 1959, 1970, 1981, 1987, 1998 then 2009 (as 2000 was leap it did not disturb the 6, 11, 11 sequence). Then add 6 to give the present year, 2015, next add 11 and 11 to give 2026 and 2037, then 2043, 54, 65; 2071, 82, 93, 2099. However 2100 not being leap changes the sequence in this case to make three six-year intervals in a row, 2093, 2099, 2105, 2111, before settling back to 2122 and 2133 followed by 2139, 50, 61 ... The six year interval spanning the century includes just one leap year. The same happens around 2200 with 2189, 2195, 2201, 2207. But at 2300 (as happened at 1900) there is a twelve-year gap, including two leap years, in place of an eleven-year one including three: 2285, 2291, 2303, 2314, 2325, then 2331, 2342, 2353. Similarly 400 years earlier the sequence ran 1874, 1885, 1891, 1903, 1914. 2400 being leap means the 6, 11, 11 year interval sequence runs through it undisturbed, as happened at 2000. Regards, Andrew James Secure Meters (UK) Ltd. is a registered company in England: 2199653 Secure House, Moorside Road, Winchester, SO23 7RX This correspondence is confidential and solely for the intended recipient(s). If you are not the intended recipient, you must not use, disclose, copy, distribute or retain this message or any part of it. If you are not the intended recipient please delete this correspondence from your system and notify the sender immediately. --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
