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Corrected:

How would one punctuate this correctly?

One of my parent's friend's houses.

Isn't it one house? One parent's friend?
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We have these choices:

One parent, one friend, two houses: One of my parent's friend's houses.
One parent, two friends, two houses: One of my parent's friends' houses.
Two parents, one friend, two houses: One of my parents' friend's houses.
Two parents, two friends, two houses: One of my parents' friends' houses.

One parent, one friend, one house: One of my parents' friend's house.
One parent, two friends, one house: One of my parent's friends' house.
Two parents, one friend, one house: My parents' friend's house.
Two parents, two friends, one house: My parents' friends' house.

If anyone would care to double-check these, I'd be obliged. Now I have to go and lie down for just a little while...
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Mister MicawberOne parent, one friend, one house: One of my parents' friend's house.

If anyone would care to double-check these, I'd be obliged. Now I have to go and lie down for just a little while...

Hi Mr Micawber

Just one correction: One of my parent's friend's house. However, since one of requires a plural, I consider the sentence ungrammatical as parent is singular. We can't say: one of my parent, we can only say one of my parents. Of course it can be in the genitive as well: one of my parents' friends.

To convey the idea you are trying to express, I would say: the house of my parent's friend or my parent's friend's house.

CB