Onside Punt after a safety?

[GAHSUMPIRE]

Hello again everybody, it has been a while since I frequented these pages. I had to drop out of officiating for family and work considerations for a couple years, but I am getting back into it. Attended the first meeting of the year tonight, and the associate gives a month quiz as a way to continue studying.  There are a number of questions I am working through, but this one kind of got me thinking, so I thought I would see what people on this board thought:

TRUE or FALSE: After a safety Team A will kick from their 20 yard line to Team B. Using a punt for the free kick Team A is prohibited by rule from performing an on side kick. 

Here are my thoughts: There is no rule that prohibits a team from doing this. If K (P?)  punts the ball such that  it hit the ground and travels 10 yds, it would meet the requirements of an on side kick. HOWEVER, when a team punts in a "normal" punting situation, unless R is the first to touch it,  the ball would be dead upon K's recovery.

Does the fact that the punt is used as a free kick change the rules?

(I realize that an onside kick from K's own 20 is probably not very likely in any case, and even less likely to be attempted using a punt, but  the question was not whether it was either possible or wise, but whether it was prohibited by rule. I am torn between the opinion that an onside kick on a free kick after a safety is legal, and the fact that possession cannot be maintained after a punt unless R touches it.)

Is a free kick a free kick regardless of the type of kick used to perform the free kick?

Sorry for the long-winded confusing question, but I am just getting back into the swing.

God Help Me, I Do Love It So.

[Magician]

A punt is not awarded to be B because it's a punt. It's awarded because it's a scrimmage kick. A punt is just one kind of a scrimmage kick. A place kick (i.e. field goal) and a drop kick are also allowed. In your question it's a free kick so it can be legally recovered by either team after it has gone 10 yards and touched the ground. A free kick can be a place kick or punt after a safety. The kicking team could definitely attempt an onside kick using a punt after safety. It would be very risky but it could be done.

[Ralph Damren]

The use of a punt after a safety for an onside kick is dampened by 6-1-2 ...When a punt is used following a safety, the ball must be kicked within one step of K's free-kick line.
Where players can enter the NZ once the ball is kicked, this prevents the punter from dropping back to his 10 and kicking a "grounder" where his teammates may reach K's 30 before the ball. It would seem much easier to kick a grounder off a tee than from a punt.

And remember, guys, that a punt following a safety that goes untouched OOB warrants a  .

[GAHSUMPIRE]

Thank you gentlemen. I figured I was overthinking things.