どこに入れたものかな?
I wonder where I should put you?
The context is deciding which class to place a student in. I have two problems:
Why is 入れた in the past tense? At the time this sentence is spoken the decision has not been made.
What is the function of もの?
I've checked all the usual questions on もの and ものか but I haven't been able to figure out how it works in this sentence.
