A traditional computer science question to illustrate how someone approaches a software problem is a quick sort for numbers. Here are some traditional algorythms by computer science profs:
http://ciips.ee.uwa.edu.au/~morris/Year2/PLDS210/qsort.html
http://linux.wku.edu/~lamonml/algor/sort/quick.html
http://pages.stern.nyu.edu/~panos/java/Quicksort/
This one interactively demonstrates how the sort works step by step
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