Dancing partner Puzzle

Julie invited couple of friends for an evening of dance, great food and fine wines. Each of the guests was handed over numbers from 2 to 18 with the number 1 reserved for Julie. Over the course of the dance Julie observed that the dancing partners numbers add up to perfect squares e.g. if number 1 is paired with number 8 then the total is 9 (8 +1) which is a perfect square of number 3.

If all the pairs add to perfect square what is Julie’s dancing partner’s number.


Courtesy: Car Talk