Google Hashcode is a Competition that takes place around February - March every year.
Teams from all over the world can participate, and they are composed by up to 4 people.

The problems that Google presents are definitely Real-World and non-trivial, but the biggest challenge is that they should be solved in less than 4 hours.

Here are the problems proposed in past editions.  They seem to be mostly optimization problems, and I think that could be suitable for the retreat since they should be solvable in the amount of time we have.
https://hashcode.withgoogle.com/past_editions.html

The link contains 5 problems, with a small description of each one. The full problem statements and associated datasets are also downloadable.

Also I was thinking to participate to the next Google Hashcode, so it could be interesting to see if those problems are actually solvable that quickly.