א שווערע חתם סופר

The Gemoro (Megillah 14a) says קרייתא זו הלילא. Reading the  Megillah is the saying of Hallel. We don’t need to say Hallel on Purim,  because reading the Megillah, is considered as the Hallel.

The מאירי says, if someone didn't read (hear) the Megillah, he must say Hallel on Purim. (to at least be Yotzei Mitzvas Hallel)

The Gemoro (18b) says that R.Meir didn’t have a Megillah on Purim, so he  wrote one by heart. 

The Chasam Sofer (Shu”t O.Ch. 192) brings a Kushya from R. Yehuda Osad zt"l

"Why couldn’t R. Meir have said Hallel instead of writing a whole Megillah?"

The Chasam Sofer answered him a Tirutz.

My Eidem asked, that "The Kushya doesn't even begin and 

why the need of the Chasam Sofer with a Tirutz?

The Gemoro only says , by reading the Megillah you were

Yotze Hallel , and not that by saying Hallel were you Yotze

Mikra Megillah."

R. Meir would not have been Yotzei Mikra Megillah by saying

Hallel and therefore had to write a Megillah.

 הפלא ופלא שהוא פלא עצומה שאין עליה תירוץ ודו״ק on the two 

Gedolim , R Y. Osad & the Heiliger Zaida.

Umitzva Leyashev