Because of the difficulty of using it, I decided that problem number 1 should be written in BrainF. It took most of the morning, but I have succeeded at this task. I unfortunately needed to compromise my rule of "programs must output the solution, not an intermediary value needed to compute it", but because the intermediary value was extremely easy to parse into a solution (I output a number of characters equal to the solution), but it would have been incredibly difficult to actually print a number, I decided to stick with the intermediary version. My next problem will be done using a much more sane language...maybe something like Haskell, which I have never used, though it is a language that is actually meant to be used.
edit: I did not compromise my rules, the number is printed in unary.