In order to prevent this, i'll explain the easiest way I found for quickly noticing if the pokemon ivs are for a HP fire or not.
YES I HAVE NOTHING BETTER TO DO IN MY LIFE
I'll put there the calculus behind all this in spoiler, you can skip them and go to the final result.
The formula for the HP type is
a,b,c,d,e,f are the remainder of the division by 2 of the ivs of the rispectively things: hp, attack,defense,speed,special attack,special defense. They can be 0 or 1
if HP is between 8 and 9, HP is fire.
We want to find all positive integer numbers X that 15X/63 is between 8 and 9.
All possible numbers are 34,35,36,37.
there is a single way of rappresenting every number in the binary sistem.
34 = 32+2= 100010
35= 32+2+1= 100011
36=32+4 = 100100
There is a biunivoque correspondence between a,b,c,d,e,f and the value of the bits.
f= First bit from the left
e= Second bit from the left
b= Fifth bit from the left
a= Last bit
As you can see, e=d=0 and f=1 in all combinations. So it means Speed and Special atk. must be even, and special def must be odd.
You can see that atk and def can change in the combinations, but still atk+def is always 1
And finaly, hp parity doesn't matter
Hp: X (any is ok)
Attack+Def= odd (12+13 is ok, 12+15 is ok , 15+15 is NOT ok)
Speed = even (for example 2,4,6,8, ..30 are ok)
Sp.atk = even (for example 2,4,6,8, ..30 are ok)
Sp.def = odd (for example 1,3,5,17, ..31 are ok)
I'll may add up some examples with screenshots if they are needed