Machine Learning and Neural Networks for High School Students I hope this question is appropriate for this forum.
In this summer I am giving a 3-day workshop on machine learning and neural networks for advanced and very enthusiastic high school students which all know at least one programming language.
Typically a day consists of 2 hours lecture in the morning and later the students should solve a given problem (with help, of course).
For the first day we are going to sove a simple pixel counting problem in a picture (Or do you know any simpler interesting example)
For the second and third day I wanted to give them a more challenging problem:
Consider the set of binary $3\times 3$ matrices. One can imagine every matrix as a chessboard like picture where every $1$ corresponds to a black field and every $0$ to a white field. The objective is to count the connected components.
I allready produced the matrices and computed a neural network. It seems to work (training set 50%), however I am not an expert in machine learning so my solution is most likely not good!
So my questions are:

Has anybody allready computed a neural network for the problem above and is willing to share his data?
Do you know similiar problems accessible for high school students which are better suited for this occasion?
For high school kids, I think the most important goal is to make sure they're impressed by what they've accomplished. To do that the task needs to be inherently useful. Classic things like the XOR problem or pixel counting aren't going to do the trick, because you're relying on the students to connect the dots and realize that this means you can build it into something cool. You need them to build a system 


that does something cool,
which can't easily be accomplished with a handbuilt algorithm,
that seems to behave intelligently.


A few ideas:


Make an environment where agents play a game. Something like tic-tac-toe or rock-paper-scissors is probably best. At the end of the course, you can let the agents that the students have made battle each other in a tournament.
Create a simple a-life environment with 2D creatures with simple sensors and joints. Let students create the neural network for the creatures, so they learn to walk. You can also let them evolve the network topology when creatures mate.
A car driver. Again, this is best with an artificial environment, but you can probably get a dataset somewhere too. This is an example from Tom Mitchell's machine learning where they did this with an actual car and a human driver for the network to learn from.