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Cycling Squares

Age 7 to 11 Challenge Level:

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


circle of numbers from top going clockwise: 14, 2, 7, 9, 16, 20, 29, 35.

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?
 

Numbers given: 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 14, 15, 7, 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.