In one of his usually unusual Maigret novels, Simenon manages to engage the reader in a detective story where there is a solution to the crime, but where the murderer and attempted murderer gets away and where the detective and the victim establish a  knowing relationship that endures.  Maigret at his best gets inside the minds of the murderer and the victim (the second victim is the eponymous ‘down-and-out’ and he survives) and the novel depicts how Maigret does so by simply walking around, poking here and there, and talking for great length with the various players.  The Bum lives under Pont Marie, so the reader gets a lovely view of the Ile de St. Louis and the quays along side of it.  Fine Maigret.