You can save highscores with the UserInfo-class!
Following code I copyed from the scenario http://www.greenfoot.org/scenarios/8385:
UserInfo ui_=UserInfo.getMyInfo(); // gets the UserInfo of the current user
if(ui_!=null) // Checks, if a UserInfo could be called
{
ui_.setScore(Greenfoot.getRandomNumber(10001)); // sets the Score
ui_.store(); // saves the score
}
It's not very complicated!
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Survive!