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Math time!

You've answered: X is 10.

Congratulations, you got the right answer. But Doom doesn't care about being right at times.:)

Depending on how the damage is delivered, the answer could be anywhere from 10 on down.

I'll explain:

If the 150% damage is dealt all at once, then the math goes like this:

Split the damage, 2/3 to health, 1/3 to armor.

      100% armor,    110% health.
     - 50% armor,   -100% health.
     = 50% armor,     10% health.

So the correct answer is 10.

But, if the damage is delivered in smaller bursts, things change.

Say it's dealt in 10% bursts (like someone who cheated and used my ARMOR.WAD from the previous answer would do:)

Split the damage, 2/3 to health, 1/3 to armor.

      100% armor,    110% health.
     -3.3% armor,   -6.6% health.

Hang on, there's a problem right there. Doom does not like non-integers. So it makes things neater by rounding the damage to health up and the damage to armor down.

      100% armor,    110% health.
     -  3% armor,   -  7% health.
     = 97% armor,    103% health.

So if you repeat that 15 times (10*15=150), you get this:

      100% armor,    110% health.
     - 45% armor,   -105% health.
     = 55% armor,      5% health.

And it always rounds health damage up. If the damage is delivered in 5% bursts (again, like one might with armor.wad):

      100% armor,    110% health.
     -1.6% armor,   -3.3% health.

Which becomes:

      100% armor,    110% health.
     -  1% armor,   -  4% health.

Repeat 30 times (5*30=150) and you get:

      100% armor,    110% health.
     - 30% armor,   -120% health.
     = 70% armor,   -  5% health. (Dead)

So I bet all of you geniuses who downloaded the demo WAD and tried it there feel a bit silly now, don'tcha?:)

Next question!

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Run along home.
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