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Jimmy's return to his room above Mike's café is an important plot point in the story. One of the things we learn is that there is a button belonging to Ben Price on the floor. Why does O. Henry choose to include this detail?
O. Henry wants to suggest Ben Price's appearance later in the narrative.
O. Henry wants to remind us to make sure our buttons are sewn on tightly.
O. Henry wants to point out that Mike needs to do a better job of sweeping his café.
O. Henry wants to demonstrate that Mike is observant.
Probably the 4th one.
Or the first. I haven't read the story so you'll have to decide which fits better.