Here's the deal,
Large sized adamantine +3 falchion. It's getting impervious added after initial creation.
Large Size (x2 hp)
Adamantine (20 hardness/+1/3hp)
+3 (+2 hardness/+1 and +30HP/ +1)
Impervious x2 hardness bonus and x2 hp bonus
So in what order do you do the math?
Is it as follows?
Hardness 10(steel) goes to 20 (adamantine) plus 12 (2 per +1 x 2 for impervious) Total= 32 Hardness
Hit Points 10 (base) x2 (large) 20 + 60 (+10 per +1, x2 impervious) 80 + 1/3 (adamantine) for a Total= 104 Hit Points.
Or is it...
Hardness of 32 as above (can't see any different math there.)
10 (base) + 60 (+10 per +1, x2 impervious) 70 + 1/3 (adamantine) 91 x2 (large size) Total= 182
Or is it different?