Challenge: sum of squares. Let's break 299

[pier4r]

Some of you may have seen the numberphile video about the "sum of squares" problem.

The problem is simple.

One has the following sequence:
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15

The objective is to rearrange them in a way that every two adjacent numbers, if added, are equal to a square of an integer number. The problem is to use all the numbers.

Example 1,3,6,10,15 (it fails then)

Don't read below if you want to give it a try.

Code:


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I personally solved it when in the video they said "it is possible to solve it". 
How a sentence can change the attitude towards a little problem.

I first listed all the possible working couples, 
then I made a "clock" with the numbers and I started to connect them.

9,7,2,14,11,5,4,12,13,3,6,10,15,1,8

then in the video they said they tested all the sequences up to 299. From 25 to 299 they found a way and likely there will be always a way.

The point is, using only real calculators (surely someone already run some programs until one million on some pc/tablet/smartphone), could we break 299 ?

I guess the 50g, prime, dm42 have good chances to break 299 if programmed in a clever way, given enough time.