## Sunday, August 09, 2020

### [govkehgg] 3+1 (threeplusone) calendar

3 days of work followed by 1 day of holiday, yielding a 4-day period.  Proportion of holiday = 1/4.

3 of the above 4-day periods followed by 1 day of holiday, yielding a 13-day period which ends with a 2-day holiday.  Proportion of holiday = 4/13.

3 of the above 13-day periods followed by 1 day of holiday, yielding a 40-day period which ends with a 3-day holiday.  Proportion of holiday = 13/40.

3 of the above 40-day periods followed by 1 day of holiday, yielding a 121-day period which ends with a 4-day holiday.  Proportion of holiday = 40/121.

3 of the above 121-day periods is 363 days, which is amazingly close to 1 year.  Add 2 or 3 days of holiday (depending on leap year), so the year ends with a 6- or 7-day holiday.  Proportion of holiday = 122.2425/365.2425 ~= 33.5% (assuming Gregorian calendar).

Current system (365.2425*(2/7) + 10) = 114.355 holidays = 31.3% .  (10 federal holidays, but many people get or take more days off, e.g., between Christmas and New Years, day after Thanksgiving.  Though many people get fewer days off as well.)

Choose the 6 or 7 day holiday to be at the end of September.  We choose to keep things synchronized with the tropical year to avoid weather that is bad for travel.