Thus, there is no thirteenth month. Rather, there is a twelfth month that occurs twice in leap years. Only Adar is suitable for intercalation for if any of the other months were to be intercalated, Adar would no longer be the twelfth month but instead the thirteenth. In that case, the mazalot would be incorrect and would not represent the two sons of Joseph.
This explanation and the Mishnah’s statement cited above (Megillah 6b) that there is no difference between the two Adars – meaning that both are referred to as the twelfth month – makes sense of the troubling Tosafot (Sanhedrin 12a) that quoted a verse in Esther regarding Adar being the 12th month (to explain why we don’t intercalate any other month).
We have not resolved whether the year of the Purim story was, in fact, a leap year or not. Hopefully, one of readers will enlighten us with a source on this matter one way or the other.