Valentine's Day!

Number Theory Level 2

As we all know, Valentine's Day is preceded by a Valentine's week, which goes like:

Feb 7 : Rose Day

Feb 8: Propose Day

Feb 9 : Chocolate Day

Feb 10: Teddy Day

Feb 11: Promise Day

Feb 12: Hug Day

Feb 13: Kiss Day.

Trevor, as we all know has a valentine apart from Math this year. So, this goes without saying that Trevor is very excited for Valentine's this year. So, he gives his valentine \(n\) Roses on Rose day, Proposes her \(n^2\) times on Propose Day, and so on. (Feb 13 was really good for him ;))

If he interacted 254 times with his Valentine during this week, How many teddies did he give her?

Details and Assumptions

You may assume that Trevor is very rich

Interaction implies Giving a rose, Giving a teddy or.., you know.

He did not interact with his Valentine apart from the information given in the question.

This problem is original.


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