Origami Challenge is another one of those challenging games from 505games that I highly recommend. It's a virtual Origami puzzle game similar to Paperama but with more levels. Each level requires the player to fold the paper into a target shape using limited numbers of fold.
There are over a hundred levels to solve in this game but you can only unlock a level upon beating the the level before it with minimum of 1 star rating. The game has a hint system that you can use if you got stuck but it costs real money thru in-app purchase. Or you can just search the web for
Origami Challenge walkthrough like the one I have below.