The holiday of Purim is observed today with a fast day called the “Fast of Esther” that precedes it on 13 Adar. Some Jews observe the fast day from morning until sundown. It does not begin the night before as Yom Kippur and Tisha B’Av, and is, in essence a half day fast. 
Esther 9:31 has been interpreted by people to state that the Judeans consented to observe this fast of 13 Adar. The verse states that the Judeans in the days of Mordecai and Esther agreed to observe Purim “just as Mordecai and Esther the queen had instructed them and just as they had accepted upon themselves and their descendants the matters of the fastings and their cry.” The problems with this interpretation, that “the fastings and their cry” are associated with Purim, are: (1) The quoted words seem to imply that the Judeans accepted the fasts and cry before agreeing to observe the two days of Purim. (2) Mordecai and Esther did not request the Judeans to fast. (3) The word is not “fast” in the singular, but “fastings” in the plural. (4) The fast of Esther on 13 Adar was introduced into Judaism centuries after the lives of Esther and Mordecai.
There is no indication in any document that 13 Adar was a fast day in ancient times. To the contrary, beginning in 161 BCE, the day was celebrated as a happy day commemorating the victory of the Hasmoneans against the Syrian general Nicanor, and was called Nicanor Day. Mitchell First shows that the Fast of Esther replaced Nicanor Day centuries later. It was first mentioned in Jewish literature in the eighth century.
Since the fast did not exist during the days of Mordecai and Esther, the notion that the Judeans accepted their request to fast on 13 Adar is untenable. A better interpretation of verse 9:31 is that the author of Esther is suggesting that the Judeans felt it was inappropriate and even impermissible to create a new non-biblical holiday. They understood that the Bible forbid them to add to or diminish what is in the Torah. Deuteronomy 4:2 states “You must not add to the word that I command you, nor may you diminish it, you must keep the commandments of the Lord your God that I command you.” Esther’s author implies that Mordecai responded, “We have already added days of worship to those mentioned in the Torah. For example, the four fasts mentioned in Zechariah 8:19 that commemorate the destruction of the first and second temples.” Mordecai’s argument was irrefutable and the Judeans agreed to observe Purim as they observed “the matters of the fastings and their cry.”
As an aside, we might
note the conjecture of Abraham ibn Ezra. He recalls that Esther fasted for two
or three days in the month of Nissan
while the current observance is to fast on only a single day, 13 Adar, which
occurs eleven months later. He supposes that originally the Judeans fasted the
same fast as Esther for the same period, but the rabbis later changed the fast
to 13 Adar to commemorate the fear the Judeans experienced when they thought
they would be killed on that day.
 We no longer know why the four other fasts are different than the fasts of Yom Kippur and Tisha B’Av, which go from evening to evening. Most likely, although this is only my guess, it is because Jewish ancestors considered the four fasts less important.
 The words “and their cry” means and the lamentations associated with the disaster that occurred.
 Nicanor day is mentioned in I Maccabees 3:57, II Maccabees 15:36, Megillah Ta’anit 12, Babylonian Talmud Ta’anit 18b, and elsewhere.
 “The Origin of Ta’anit Esther,” AJS Review 34:2, pages 309–351. We do not know why the rabbis invented this fast day and replaced Nicanor Day. Perhaps it was because they disliked Nicanor Day, a non-religious celebration instituted by the general public, because it celebrated a victory by human efforts with no indication that God was involved. In contrast the rabbis saw Esther’s fast as a petition to God for divine aid which they were convinced God granted.
 See the Babylonian Talmud, Rosh Hashanah 28b, Eruvin 95b–96a, Megillah 2b, and elsewhere. While the rabbis accepted this law not to add to the biblical commands or cease observing any of them, they never implemented this law. I showed in my book “Mysteries of Judaism” that they changed every biblical holiday without exception.
 One cannot go without food and drink for three days, so in his commentary to 4:16, ibn Ezra states that she fasted two days.