Focus on competitive coding/problem solving. They do not expect college graduates to have projects. Also, in general it is difficult to judge someone based on the project unless the project is already a hit but in that case why do you really want a job.

Puzzle/problem solving type questions are easy to help them "filter" people. It doesn't mean anything -- do not read too much into it. Its just an easy way to select few from some people.

So, prepare those puzzles, and you are good to go. Almost all of them will ask those.