Allright. Lets make a game. And lets make it easy to build, but it'll still be a game. 2048 has been popular, and it's really really simple. You have a 4x4 grid, with numbers in it. You can slide all the tiles in the grid to the left, right, up, or down, and the numbers on two tiles match (in the direction you slide), they merge together to form a new tile, with a value that's twice the old tile. The game is free in the app store -- play it a bit, and see how it works!
Go ahead and have buttons for the four different sliding directions (we'll get to gestures later -- no need to handle them now unless you want)
Arrange 16 labels to show each of the grid spots (or make objects if you want -- style points count!). IBOutletCollection, and tags, are going to be your friends.
There will be a little bit of logic to figure out how the tiles merge together, and you'll need to write some code to insert new tiles.
The game is over when you can no longer make a move!