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The three day fast: 
Esther, upon agreeing to Mordechai’s request, asked that all the Jews in Shushan fast for three days.
When did the three day fast take place?
It took place over Pesach, on the 14th-16th. That year the Jews in Shushan did not eat Matzah.
Why did Esther specifically ask the Jews of Shushan to fast?
She requested that all the Jews of Shushan that partook in the feast of Achashveirosh now fast as repentance for that sin.
Was Mordechai reluctant to agree to the fasts?
At first Mordechai responded to Esther that it is forbidden to fast in the month of Nissan, especially on the dates of Pesach, and he does not have power to revoke this prohibition. Esther replied “You are an elder of Israel. If the Jews will be annihilated what use are the Mitzvos; What use will be the Torah”.
How did they fast for three days straight?
They would have a meal each day prior to the next day’s fast.