Dirk Gently's Holistic Detective Agency (original 1987; edition 1991)

Wikipedia description: Dirk bills himself as a "holistic detective" who makes use of "the fundamental interconnectedness of all things" to solve the whole crime, and find the whole person. This involves running up large expense accounts and then claiming that every item (such as needing to go to a tropical beach in the Bahamas for three weeks) was, due to the "fundamental interconnectedness of all things", actually a vital part of the investigation. Challenged on this point in the first novel, he claims that he cannot in fairness be considered to have ripped anybody off, because none of his clients have paid him yet. He maintains an office at 33a Peckender St. N1 London, with telephone number 01-354 9112 (407-2882 in the advertising campaign for the book).
Gently has an odd facility for accurate assumptions, as every wild guess he makes turns out to be true. Once a student at St. Cedd's College, Cambridge, he left in disgrace when he attempted to acquire money by selling exam papers for the upcoming tests. His fellow students were convinced that he had produced the papers under hypnosis—in reality, he had simply studied previous papers and determined potential patterns in the questions. However when his papers turned out to be exactly the same as the real papers, to the very comma, he was arrested and sent to prison.