What ENGLISH-language free online arvchives (with online-judges) with VERY EASY problems can you propose? Level of problems should be NOT for olympiads at all, but for very beginning of programming; the desired difficulty level is smth like (Russian-language) http://informatics.mccme.ru/mod/statements/view.php?id=276 (exercises to use if statement) or http://informatics.mccme.ru/mod/statements/view.php?id=208 (exercises to use 1D array).

If OJ contains both hard and easy problems, it's REQUIRED that easy problems are already selected to clear separate lists. The situation like as "anyone can try a lot of problems and choose easy among them" is NOT what is required.