Addicting games

One of the most addicting games in recent times has been 2048. The game starts out with a grid of tiles that you can slide in any direction to combine them. You must keep adding tiles until you reach the 2048th tile. But is it possible to get to the 2048th tile? The game uses an algorithm that will never let you move more than 16x16 tiles without either running out of moves or having the position exceed the upper limit of 32768, which can't be represented in a signed 16-bit integer. But there are some strategies you can use to make your way up to...