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August 1

March y to September y = August y+1 to February y+2

This year, August 1 is a Thursday, and last year, March 1 was a Thursday. In general, why do March 1 to September 28/29 in year y correspond to August 1 in year y+1 to February 28/29 in year y+2 if year y+1 is not a leap year? GeoffreyT2000 (talk) 13:57, 1 August 2019 (UTC)[reply]

Because there are only 14 possible calendars, AND 365 MOD 7 = 1. In a non-leap year, if the year has March 1 on a Thursday, that MUST be the calendar of a Common year starting on Monday. Because 365 MOD 7 = 1 (that is 365 divided by 7 has a remainder of 1), that means the year bumps FORWARD one day per year, so the NEXT year will be a Common year starting on Tuesday, and March 1 is Friday. Since March 1 and August 2 are always on the same day of the week (check all 14 calendars. It's always true) that means that (barring a leap year) August 2 last year is the same day of the week as August 1 this year (because of the 1 day shift every year) AND that's why August 1 last year has the same day as March 1 last year. --Jayron 32 15:56, 1 August 2019 (UTC)[reply]

This results from the pattern within a year. From 1 March of year y to 1 August of year (y + 1) (where (y + 1) is not a leap year) is 365 + 31 + 30 + 31 + 30 + 31 = 518 days. This is an exact number of weeks. The answer to the second question lies in this plus the fact that any period of five months which does not include 1 March and the day before always contains 153 days. So if you choose your starting date judiciously you can extend the correspondence to a maximum of seven months. 2A00:23C5:CDAD:6500:34F0:5D70:7172:F66A (talk) 16:41, 1 August 2019 (UTC)[reply]