I think you could find that out a lot more easier if you use the "Best Paid Games" and "Free Games" sections within the inbuilt AppStore on your iPhone
Hi, Park In is the best challenging puzzle game for iphone,ipad & ipod. https://itunes.apple.com/us/app/park-in/id363488823?mt=8
Angry birds is best game for i phone. pulling the rubber is best in i phone and it is easy to play on iphone.
My Top 5 Iphone games: 1= Clash of Clans 2= Sims Free Play 3= Jarassic Park 4= 4 Pics 1 Word 5= Temple Run 2 'Geared' is also a good one!
I just got blendoku for my iphone, really fun. its like sudoku but you have to create gradient colors