Help Lucy impress Nick the math geek and find his apartment number!
Lucy a track athlete, really likes Nick, a math geek. Nick is having a party at his apartment on Saturday and invites Lucy. Lucy knows where the apartment building is but does not know the apartment number
The invitation says:
Party starts 21:00 Saturday night. My 35th floor apartment is on the side of the floor with odd numbered apartments (the hallway on my floor is shaped like a large square with the odd numbered apartments on the outside of the outside and even numbered apartments on the inside).
Apartment numbers in my building start from 1 on ground one but do not necessarily start with the floor number (except floor 1) because all whole numbers (starting from 1) and used and there are not 100 apartments per floor.
The sum of the odd numbered apartments on my floor is 7975. Because I am so cool, I live in the apartment with the largest prime number on my floor.
Each floor has the same number of apartments
There are between 13 and 44 apartments on each floor
Don't ask Lucy to use her athleticism to run around the floor and knock on every odd number door to find him. Nick would consider that cheating