In some colleges students are let to use an IDE and Internet and in mine you have to write down your solution in paper.

As far as I know, it's pretty much impossible to make a correct non-trivial program on the first try. I'd be fine with no using computers if my teachers assessed my approach instead my code -literally-... that's not the case unfortunately.

Which ones are more usual, 'written' or 'coded' exams? And which way is the most adequate?

Edit - question title changed (it used to be Should students have the right to do exams using a computer?)