Challenge requires concentration so it would mean that it wouldnt do anything under Rage I guess guess right?
If Cavalier have +4 enhancement STR bonus from an item and (sighs players do have such imagination) and also the mount have a +4 enhancement bonus from an item I would assume that even when using the Order of the Sword ability it wouldnt stack those +4 enhancement bonus from the rider and the mount right?
If the mount have Pounce he shouldnt be able to use it if the rider is on him right?
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1) As written, yes, you are correct. A Cavalier could not go into a Rage and use Challenge at the same time.
2) I don't believe this is correct. Adding the mount's strength modifier is not the same thing as adding the strength score (in which case I would rule the two wouldn't stack). As written, it seems the cavalier would indeed benefit from having both himself and his mount equipped with a belt of strength.
3) Yes, a mount can totally pounce while being ridden. It's the reason Raptor and Tiger mounts are so awesome, if you take the Beast Rider archetype.
*Edit: Also, why would you choose either of those options when you could ride a freakin' bear! (Warning: link contains adult language)
