What are some of the most interesting algorithmic problems you have faced?

Data acquisition for calibrating a sensor. The calibration itself is easy, the problem is I don't have control over the samples, it just gets one aftet another and has to decide whether its useful for the calibration or not (by some measure). And then it needs a stop condition, determining when there's enough samples. All this needs to run on a small microcontroller with very tight memory limits.

In France we have this contract that allows a student to go a period of time in a company, and the rest in the school so that he already has some experience when he finishes his studies.
The problem is that sometimes, student struggle to find a company that accepts to take him in part time. So we thought about an algorithm that would automatically send the student's resume to companies the student's school is used to deal with, and only companies that are officially looking for guys who knows specific technologies, so it would accelerate a lot the 'find a company that suits you' procedure

Good memory: I managed to put this in place with a good ol' Symfony
Bad memory: the company I worked with seems to be dead for now, and I read recently that some other start up is either stealing the idea or found it by themselves.