Can Rosh Hashanah fall on any day of the week?

The Jewish perpetual calendar was arranged in a manner which ensures that the first day of Rosh Hashanah will never take place on Sunday, Wednesday or Friday. This guarantees that Yom Kippur will not fall on a Friday or Sunday, which would produce two consecutive days when preparing food and burying the dead is prohibited, and that Hoshanah Rabbah will not occur on Shabbat, which would interfere with the custom of taking the willows on this day.