Math puzzle Extreamly hard can you help me?

Question

The puzzle says that you have to draw 15 circles like this:
( )( )( )( )( )
( )( )( )( ) You have to put the numbers 1-15 into it.
( )( )( ) You can't use any number twice
( )( ) and you have to subtract the two numbers
( ) like this :

(15) - (14) - (2) - ( 8 ) - ( 3 )
( 1 ) - (12) - ( 6 ) - ( 5 )

15 - 14 = 1, the 1 goes directly below the two numbers.
(15) - (14) - (2) - ( 8 ) - ( 3 )
( 1 )
14 - 2 = 12 ,the 12 goes directly below the two numbers.
(15) - (14) - (2) - ( 8 ) - ( 3 )
( 1 ) - (12)
12 - 8 = 4, the 4 goes directly below the two numbers.
(15) - (14) - (2) - ( 8 ) - ( 3 )
( 1 ) - (12) - ( 6 )
8 - 3 = 5, the 5 goes directly below the two numbers.
(15) - (14) - (2) - ( 8 ) - ( 3 )
( 1 ) - (12) - ( 6 ) - ( 5 )
And so on and so fourth.

Please help,
John

Answer 1

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

Of course the mirror image of this will also work:
(6) (14) (15) (3) (13)
(8) (1) (12) (10)
(7) (11) (2)
(4) (9)
(5)

There are no other solutions.

I have to admit there's no elegant logic here, I just coded a routine to brute-force it after playing around with it for a bit and convincing myself that I wasn't getting anywhere.

Answer 2

Whoa..........
good............luck..................