+

A lady invites 17 friends over to dance. She gives everyone a number from 2 to 18 which she pins on their backs. She has the number 1 pinned to her back. Everyone picks a dance partner. Someone notices that if you add the numbers on any two people that are partners you get a perfect square. For example, a given pair might have 4 and 5 which sum to 9 which equals 3^2 (a perfect square).

Question: What is the number on the back of the hostess' partner?