If you need to write something cool from scratch to "impress" other students, one cool idea would be to make something they'll find useful or funny, amd that they'll use after the competition is over.

From the top of my head, wjen I was a student:

- RSS feed reader
- 2D platform game
- Sharing platform for documents
- ...

Now if they're more geeky, amd you want to go with CLI, you can make more specific stuff, like the following:

- coreutils subset
- text editor
- picture renderer with ascii blocks
- ...

Now for ideas that I find useful:

- automatic filesync between hosts (torrent based)
- deduplication + compression software
- mk(1) and redo(1) implementation in C