When Purim Was on Pesach

Although the events of the Purim story transpired over a lengthy period of time, the main action occurred over a few days. The Megillah specifically states that Haman’s letters stating that the Jewish nation should be decimated were sent out on the 13th of Nissan. Mordechai responded by asking Esther to immediately request an audience with Achashveirosh. Esther agreed on the condition that the Jews in Shushan fast for three days. The exact timeline at this point is not so clear.
The Gemara states that the three-day fast occurred on Pesach. Mordechai’s directive to fast caused the Jews to override the prohibition against fasting on the first day of Pesach. The Beis Yosef cites an opinion that fasting on Chol Hamoed is biblically forbidden. Yet, the Gemara did not mention that this prohibition was overridden during the times of the Purim miracle. One possible interpretation of the Gemara is that the Jews fasted on the 13th, 14th, and 15th of Nissan. They only fasted on one day of Pesach, namely the 15th of Nissan. They did not fast on the 16th of Nissan, which is considered Chol Hamoed according to Torah law.