The handwriting in these bills and letters seem to belong to the same person or seems

the sentence does not violate the phrase structure second rule (introduced by noam chomsky) because noun phrases consist of a determiner such as a, the or every, and a noun. in the sentence, the noun phrase the cake includes a determiner (the) and a noun (cake).

on the other hand, the first rule indicates that a sentence encloses a noun phrase, followed by a verb phrase. the example sentence can be analysed as follows:

john (n) + ate (v) + the (det) + cake (n).

mark twain, real name samuel langhorne clemens, was an american writer, humorist, entrepreneur, publisher, and lecturer. among his novels are the adventures of tom sawyer and its sequel, the adventures of huckleberry finn, the latter often called "the great american novel". wikipedia