The answer is 354, 11 days fewer than the solar calendar. Judaism and Islam, which both observe a lunar calendar, treat this disparity differently, explaining why it is so noteworthy that this year, the Muslim holy month of Ramadan is expected to begin on the same day as the Jewish new year, Rosh Hashana (Oct. 4).
Many Jewish holidays, including the fall harvest festival of Sukkot and the spring observance of Passover, are connected to agricultural and seasonal cycles. It would be unacceptable for these holidays to "migrate" throughout the year, celebrating Passover, for example, during the coldest time of winter.
To correct for this problem, every three years (when the 11-day annual discrepancy between the solar and lunar calendars totals around 30 days) the Jewish calendar inserts a 13th month into its cycle.
The Muslim calendar, however, follows a strictly lunar schedule of a 354-day year because Islam's major holidays are not connected to specific seasons or agricultural harvests.
Accordingly, Ramadan and Rosh Hashana begin on the same day only once every 33 years.