Cycling squares

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



 

In the circle of numbers below, each adjoining pair adds to make a square number:

 

Image
The following numbers in a circle: 14, 2, 7, 9, 16, 20, 29, 35, 14.

For example,

$14 + 2 = 16, 2 + 7 = 9, 7 + 9 = 16$

and so on.

Can you make a similar - but larger - cycle of pairs that each add to make a square number, using all the numbers in the box below, once and once only?

2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 14, 15, 17, 19, 21, 28, 30, 34.
 
You might find it helpful to print off and cut up these cards of the numbers so you can move them around to try out your ideas.