Hi All, I need some help to solve this problem.. Assume you have n=1,2,3,...,15 number. Put them in an order so that when you add two successive number you get perfect square. As seen one example below. 9+7=16, 7+2=9, 2+14=16, and so on. I did this using pen and paper work.. I tried to solve this using Mathematica. First I got a set of number that make each number perfect square.. But I don't know what should be next step. I tried to use graph but it takes time and is easy to make error (has not been completed yet). I also want to extend it to say n=25.. Any help appreciated. Thanks..

when n=15---->9-7-2-14-11-5-4-12-13-3-6-10-15-1-8

when n=16----> 16-9-7-2-14-11-5-4-12-13-3-6-10-15-1-8

when n=17----> 16-9-7-2-14-11-5-4-12-13-3-6-10-15-1-8-17

when n=18----> no sequences

when n=19----> no sequences

when n=20----> I claimed no sequences

It Must start with 18 since there is only one number make it perfect square namely 7. 18+7 but after this we have two options. 18+7+2 or 18+7+9

Please see attachment..