Do you want to get the student interested in programming or do you want to show what freshman CS students have to put up with? Because I think these are two pairs of shoes, and personally I would get bored after doing even just one sorting or text conversion problem.
My suggestion would be to choose something that has a nice visual result, either directly on the command line or after visualizing it with something like gnuplot/matplotlib. One of my favorite "beginner's problems" for potential research assistants with little to no programming experience is to code up a simple diffusion-limited aggregation simulation (https://en.wikipedia.org/wiki/Diffusion-limited_aggregation). The algorithms are simple (less than 100 lines of Python), there is plenty of documentation around, and the results are nice to look at.
