We should incentivize people to focus less on the problems they can easily solve and make them push the boundaries of their abilities. I understand that these problems are for training purposes. However, there is also obviously a competitive background behind our training here. We otherwise wouldn't have a rank on our profiles based on the number of solved problems.
Such a system is also present on one of my favorite websites: http://spoj.com
Essentially, every user gets a score. The score is computed by summing up the scores for each task. A task is scored based on the number of people that solved it up to a minimum of 1 point. Example:
10 people solved it = 10 points
>10.000 people solved it = 1 point.
Benefits: