Dear Bais Din:
Although we are to recite 100 blessings daily, how many times must we answer AMEN?
Although there is no Talmudic source that indicates the number of times Amen should be answered each day, and it is no mentioned in the Ramban or Shulchan Aruch (see Orach Chaim 46:3 concerning 100 blessings), there are a number of kabbalistic sources that mention the requirement to say Amen 90 times daily. The primary source to mention this is Tikkunei Zohar (1st Tikkun), and it is also mentioned in Arizal (intro. to Shaar Hakdamos), and henceforth in a number of sefarim that quote the teachings of Arizal. It is usually mentioned in connection with the word tzaddik, whose constituent letters represent 90 amenim, four kedushos, 10 kadeshim, and 100 blessings, all of which should be recited or answered daily. Those halachic authorities who base rulings on kabbalistic sources mention the concept of 90 amenim as obligatory (Ben Ish Chai, shanah rishonah, Vayeishev 15; Kaf Hachayim 15:51).