I wanted to learn how to make an iPhone app in Objective-C. My group at the EA Code Jam went from not knowing Objective-C to a playable OpenGL game in 12 hours. The game is pure Objective-C and OpenGL, with no additional libraries.
It’s very heavily inspired by Super Hexagon. You are the triangle, and you move by touching the left or right side of the screen. The goal is to avoid the solid blocks coming at you for as long as possible.