Here's an interesting case of HoP/Counterfeit. I can only imagine the arguments that would have happened if this game were in real life. Friends would be lost!
He plays exactly eight different cards, including the Counterfeited HoP. On the first HoP play, he can gain a Province because HoP is in play. But gaining the Province trashes the HoP. Counterfeit then plays the HoP again (even though the HoP is in the trash), but now there are only seven different cards in play because the HoP is in the trash, so he can only gain a card costing up to $7. He then plays another HoP (not Counterfeited) and now he can gain a Province again because the second HoP is in play and he's back up to eight different cards in play.
An interesting subtlety here is that Counterfeit trashes a treasure after the treasure has been played twice. So say he plays this exact same turn and Prince ($8-Action) is available. He can use the Counterfeited HoP to gain Prince on the first HoP play and Province on the second HoP play, but if he gains Province on the first HoP play then he could not gain Prince on the second HoP play because gaining the Province trashes the HoP immediately and then there are only seven different cards in play.
Joey Mann: turn 14
Joey Mann duration Lighthouse
Joey Mann plays Cartographer
Joey Mann draws Silver
Joey Mann looks at Gold, Peddler, Chapel, Horn of Plenty
Joey Mann discards Chapel
Joey Mann discards Horn of Plenty
Joey Mann discards Gold
Joey Mann places Peddler on top of deck
Joey Mann plays Peddler
Joey Mann draws Peddler
Joey Mann plays Peddler
Joey Mann draws Horn of Plenty
Joey Mann plays Lighthouse
Joey Mann plays Peddler
Joey Mann draws Counterfeit
Joey Mann plays Peddler
Joey Mann draws Hunting Grounds
Joey Mann plays Hunting Grounds
Joey Mann shuffles deck
Joey Mann draws Gold, Chapel, Horn of Plenty
Joey Mann plays 1 Silver, 1 Gold
Joey Mann plays Counterfeit
Joey Mann plays Horn of Plenty
Joey Mann gains Province
Joey Mann trashes Horn of Plenty
Joey Mann plays Horn of Plenty
Joey Mann gains Horn of Plenty
Joey Mann trashes Horn of Plenty
Joey Mann plays Horn of Plenty
Joey Mann gains Province
Joey Mann trashes Horn of Plenty
Joey Mann buys Province
Joey Mann gains Province
Joey Mann shuffles deck
Joey Mann draws Cartographer, Lighthouse, Province, Gold, Peddler