# What is the greatest number of holiday days falling on weekdays in a year?

This is a question that can easily come up for an observant Jewish person who works in the secular world and needs to calculate how many days of vacation he or she will need to take from work for Jewish holidays. I would expect that the answer would be the same for either a secular or Jewish year since the secular new year falls smack in the middle of the period between Shemini Atzeres and Purim and does not threaten to fall on the other side of either holiday, but if I'm wrong about that, I will accept the answer for either a secular or Jewish year.

For the purpose of this question, let's assume we're talking about yom tov and chol hamoed as well as including Purim and Tisha B'Av. Let's also assume we're talking about a standard American week (Monday - Friday) but ignoring civil holidays which could affect the answer. We'll ignore having to leave work early due to erev chag or erev shabbos.

Obviously, one can calculate an upper bound on this answer by simply counting all such days. I would like to take into account the realities of our current fixed calendar which may mean that certain holidays falling during the week implies other holidays fall on weekends.

If an approach can be taken to find the answer which is too much effort to actually do, I would be interested in the approach.

Between Purim and the next Shemini Atzeret the calendar is completely fixed (no leap years, leap days, etc.). The four possibilities are:

• Purim (F), Pesach (S-Sh), Shavuot (M), Tisha b'Av (S), Rosh haShana (T-W), Yom Kippur (R), Sukkot (T-T). That's 15 weekdays. (6 of complete Issur Melakha)

• Purim (S), Pesach (T-M), Shavuot (W), Tisha b'Av (T), Rosh haShana (R-F), Yom Kippur (Sh), Sukkot (R-R). That's 15 weekdays. (7 of complete Issur Melakha)

• Purim (T), Pesach (R-W), Shavuot (F), Tisha b'Av (R), Rosh haShana (Sh-S), Yom Kippur (M), Sukkot (Sh-Sh). That's 14 weekdays. (4 of complete Issur Melakha)

• Purim (R), Pesach (Sh-F), Shavuot (S), Tisha b'Av (S), Rosh haShana (M-T), Yom Kippur (W), Sukkot (M-M). That's 15 weekdays. (6 of complete Issur Melakha)

If you unfortunately aren't in Israel, then the breakdowns are:

• Purim (F), Pesach (S-S), Shavuot (M-T), Tisha b'Av (S), Rosh haShana (T-W), Yom Kippur (R), Sukkot (T-W). That's 18 weekdays. (10 of complete Issur Melakha)

• Purim (S), Pesach (T-T), Shavuot (W-R), Tisha b'Av (T), Rosh haShana (R-F), Yom Kippur (Sh), Sukkot (R-F). That's 18 weekdays. (12 of complete Issur Melakha)

• Purim (T), Pesach (R-R), Shavuot (F-Sh), Tisha b'Av (R), Rosh haShana (Sh-S), Yom Kippur (M), Sukkot (Sh-S). That's 15 weekdays. (6 of complete Issur Melakha)

• Purim (R), Pesach (Sh-Sh), Shavuot (S-M), Tisha b'Av (S), Rosh haShana (M-T), Yom Kippur (W), Sukkot (M-T). That's 17 weekdays. (9 of complete Issur Melakha)

• Great. Starting at Purim and going through Sukkot also has the added advantage of starting at the beginning of the secular year and going through the end of the secular year. So this scenario likely corresponds with many people's vacation calendars. Jan 17 '17 at 2:39
• Okay, for everyone else looking at this confused, Saturday is Shabbos, Sunday is S, Monday is M, Tuesday is T, R is Thursday, W is Wednesday Aug 14 '18 at 16:45