[WizzleKake]

I can recommend Rosalind http://rosalind.info/problems/locations/

It has bioinformatics problems. They start really easy ("count the bases in a DNA sequence") and get progressively harder.

For each problem you get some sample data to work with. When you think you've figured it out, you can download a dataset to run your algorithm against, then upload the output to see if you are correct. There's a time limit for submission, and although you can keep re-trying, the data sets are different each time.

Check it out! Don't let the bioinformatics part throw you off.