No method can solve the problem you've given without additional information.
What do you call "solving the problem"?
Any method will output some estimates. Some methods will output better estimates, some worse. As people have pointed out, this was an example of a real problem and yes, real-life data is usually pretty messy. We need methods which can handle messy data and not work just on spherical cows in vacuum.
Yann LeCun, now of Facebook, was interviewed by The Register. It is interesting that his view of AI is apparently that of a prediction tool:
"In some ways you could say intelligence is all about prediction," he explained. "What you can identify in intelligence is it can predict what is going to happen in the world with more accuracy and more time horizon than others."
rather than of a world optimizer. This is not very surprising, given his background in handwriting and image recognition. This "AI as intelligence augmentation" view appears to be prevalent among the AI researchers in general.