depends on the meaning of the whole context - plural pilgrims or a single pilgrim?
if it's a single pilgrim, then it'll be placed as follows -> pilgrim's place
if it's multiple pilgrims, then it'll be places as follows -> pilgrims' place
Pilgrim s' because when there is already a s on the end of a word (e.g Thomas = Thoma s' shoes) but if there was no s on the end (e.g Tom = Tom**'s** scarf). Hope this helped!
The placement of the apostrophe in "pilgrims place" depends on whether you are referring to a single pilgrim or multiple pilgrims. If it's one pilgrim, it should be "pilgrim's place," indicating possession. If it's multiple pilgrims, it should be "pilgrims' place," showing that the place belongs to many pilgrims.
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