zlacker

>>jeremy+(OP)
Ok, I think I may have the ultimate answer to this, a sequence that grows optimally fast. It goes like this:

Imagine 2^(7n) copies of the judge of this competition. For every judge create a different bit sequence of length 7n. Decode it from ascii and ask if it is a valid entry of the competition. Take the largest valid entry of those imaginary competitions. That is my entry. In order for this procedure to be consistent, this entry must be longer than n characters. Hence it will end with some padding you may disregard: asdfasdfasdfasdfasdfasdfasdfasdfasdfasdf.

>>im3w1l+iI
If you're allowed to submit entries that are mutually recursive with the decision procedure of the judges, I'm afraid the competition becomes less well defined. For example, it's easy to create a paradoxical entry by adding 1 to your entry. Also see Berry's paradox: http://en.wikipedia.org/wiki/Berry_paradox

>>cousin+uK
Yeah, I agree that it becomes less well defined. The problem with Berry's paradox is that it refers to itself. I circumvented paradox, by only refering to shorter descriptions of the number, than the description I gave. If that strategy works really depends on what the judge thinks though. Assuming he accepts refering to his own potential judgements of shorter sequences but not longer or equally long, the solution would work and the rules would be paradox free.