Cozy City is a puzzle game made up of binary trees with 1-3 child nodes (some might say k-ary). There is an endless amount of puzzles using this and if people are interested I'll write up more about it.
Link to game: https://itunes.apple.com/us/app/cozy-city/id947286649
Link to game: https://itunes.apple.com/us/app/cozy-city/id947286649