Post making contest 3.0

Theorem: There does not exist a post that passes rule 2, or rule 2 is completely unfair.

Proof: Suppose the opposite, that is, there exists a post which passes a fair rule 2. If rule 2 were a fair rule, then there would be more than a 5% chance of passing it (which I think is about average for the worst rules). There have been about 300 posts since the start of the round. If we assume that about a third of them have been made by Crowstone (because a post usually judges around two other posts), then there are 200 valid posts. Using the binomial distribution, then the odds that all of these would fail is .000035. This is much less than .05, so it should not happen if the rules were fair. Therefore, either rule 2 is unfair or it is impossible to pass.

■

this passes rule 3 and 5.