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Chow (1998) [7] provides a detailed analysis of a version of the paradox in which a surprise hanging is to take place on one of two days. Applying Chow's analysis to the case of the unexpected hanging (again with the week shortened to two days for simplicity), we start with the observation that the judge's announcement seems to affirm three things:
If Cheshvan has 29 days, then Kislev will have either 29 or 30 days. This is the only occurrence in which it happens. If both Cheshvan and Kislev have 30 days, then the Tenth of Tevet will occur on Friday, one of two public fasts that can possibly be observed on a Friday (the other being the Fast of the Firstborn). The fast is not broken until ...
The Babylonians invented the actual [clarification needed] seven-day week in 600 BCE, with Emperor Constantine making the Day of the Sun (dies Solis, "Sunday") a legal holiday centuries later. [2] In the international standard ISO 8601, Monday is treated as the first day of the week, but in many countries it is counted as the second day of the ...
The Rata Die method works by adding up the number of days d that has passed since a date of known day of the week D. The day of-the-week is then given by (D + d) mod 7, conforming to whatever convention was used to encode D. For example, the date of 13 August 2009 is 733632 days from 1 January AD 1. Taking the number mod 7 yields 4, hence a ...
One can readily see that, in a given year, the last day of February and March 1 are a good test dates. As an aside note, if we have a three-digit number abc, where a, b, and c are the digits, each nonpositive if abc is nonpositive; we have (abc) mod 7 = 9*a + 3*b + c. Repeat the formula down to a single digit.
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A 50-year "pocket calendar" that is adjusted by turning the dial to place the name of the month under the current year. One can then deduce the day of the week or the date. A perpetual calendar is a calendar valid for many years, usually designed to look up the day of the week for a given date in the past or future.