In all the questions there is the implicit assumption that the grammar of a language is based on a set of rules that can be reproduced and reapplied. This is hardly the case with natural languages, which, rather than sets of rules, are more like vast sets of exceptions to very few rules. While tools such as statistical analysis have been succesfully applied to analyzing languages, expecting linguistics to work like mathematics seems unnecessarily limiting.
To illustrate with an example, think of a similarly-constructed problem in English. Can you correctly deduce the missing words just by reproducing the patterns below?
ox - oxen / box - ?
mouse - mice / grouse - ?
dish - dishes / fish - ?
Separately, there's also the broader issue that languages are primarily what we speak, to which the writing conventions are secondary. In these examples, we're only looking at how things are written, which is yet another filter that gives an incomplete view.