If at first you don't succeed

...use maths.

I have finally conquered the puzzle. The solution looks something like

		5
	8	7	6
4	2	3	9	1

Every piece now has an A point, a B point and a C point. I was just about to rule out 5 as a point when the last possible combination of pieces just worked!

Assuming I've already ruled out the two other points of 5 as being the top, then:

1. 5 forces 7 at its bottom.
2. On the LHS of 7 I must place either 8 or 9.
3. On the bottom of 9 I must put either 2 or 6.
4. 2 forces 3 on its LHS.
5. 7 forces 6.
6. 6 forces 4 and then this solution doesn't work.
7. Going back to follow on from step 2, on the RHS of 7 I must put either 2 or 6.
8. If I have a 2 I can place pieces below the 2 and the 8 but then can't place a piece between these.
9. Going back to follow on from step 7, 6 forces 1.
10. 9 forces 3.
11. This solution works!