Someone on HN posted the Martyr2's mega project list: https://github.com/thekarangoel/Projects
You could take some inspiration from it.
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You could take some inspiration from it.
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.