In "A Municipal Report," what coincidences are required for the development of the plot?
I guess what they're asking is what coincidences in the story are needed to tell the story and develop a plot, but I'm not sure exactly.
One big coincidence is that one of the dollar bills the narrator gives to Uncle Caesar has been torn in half and pasted together with a very conspicuous strip of blue tissue paper. Azalea Adair sends a little girl to the store to buy tea and gives her a dollar bill with the same blue tissue paper, proving that Uncle Caesar must have given her the money right after he brought the narrator to her house. Later Major Caswell buys the narrator a drink, paying with two dollar bills, one of which is obviously the same bill with the blue tissue paper. Evidently Azalea Adair had to take that dollar back from the little girl and rescind her earlier offer of tea. Uncle Caesar must have learned about this either from Azalea or from the little girl. The woman is so poor that she can't even afford tea. She had received the narrator's two dollars from Uncle Caesar and then been forced to give them to her husband, the drunken Major Caswell, who robbed her of all her money.
The other big coincidence has to do with the unusual gold button on Uncle Caesar's overcoat. The narrator sees Uncle Caesar downtown near his hotel and notices that the big button made of unique yellow horn is missing. Then the narrator learns that Major Caswell has been murdered. He joins the crowd surrounding the body and at that point the dead man's hand relaxes and the distinctive yellow button rolls out. The narrator surreptitiously pockets it and throws it into the river the next morning. Obviously it was Uncle Caesar who was responsible for Caswell's death, either in a struggle or as deliberate homicide.
O. Henry's story relies heavily on these two coincidences involving a dollar bill pasted together with blue tissue paper and an unusual gold button which turns up in a dead man's hand. It is coincidental that the narrator is so closely involved with both objects. It is only a minor coincidence that the man who drives the narrator out to Azalea Adair's home is a former family slave who is devoted to her.
O. Henry was not a realist but a romanticist. He liked coincidences. His most famous story, "The Gift of the Maji," is based on the coincidence that the heroine sells her hair to buy her husband a watch fob and the husband has sold his watch to buy her combs for her beautiful hair.