OK, one problem with fighting in todays world. Yes, you can punch the nose, probably ruin the Gremlin's day...however, what it the Gremlin has a blood borne disease, (HIV, Hep). You might have won the battle, but the long term effects might not be what you would like...
Find out the little gremlin has hiv and you notice after you punched him that your knuckles are bleeding, you are going to spend a lot of sleepless nights "wondering".
A fast jab to the throat drops the biggest, badest, a snap kick to the knee cap will tear their knee off, months of traction, surgery, etc.
Finally, if you do want to punch the face, use a slight hook, catch them back where the jaw hinges...this will shatter the jaw with the least amount of effort!
A blow to the lower right hand side of the body, below the ribs, try a downward shot, will bruise/crush the liver...if you can crush it, they die, if it's bruised, they drop!
A blow to the side of the spine, over a little on either side, is a kidney shot, again, if you can tear the kidney, "death", otherwise they usally drop!
Now, realize that you are subject to the same effects if "they" know where/how to hit!
A thumb shoved through the eye socket will disable/kill...at the very least blind them "forever".
My advice, apologize like hell and boggy, put one foot in front of the other and get the ell" out of there...