In "One Thousand Dollar" what problem does Gillian face?

Young Gillian faces the immediate problem of spending the $1,000 inheritance he's just received from his uncle's will, of which he needs to account for every last penny. For most people, it sounds like a nice problem to have, but for Gillian it turns into a nightmare. He travels all over New York, trying to figure out a way to relieve himself of what's becoming a growing burden. On his travels he even asks a number of complete strangers what they would do with the money, but all to no avail.
Gillian finally hits upon an ingenious idea. He's going to give the money to his uncle's ward, Miss Hayden, who received only a negligible sum from his inheritance. Gillian doesn't yet know it, but he'll receive $50,000 if he's found to have spent the money wisely. However, if Gillian is discovered to have squandered his inheritance on vice, then that money will go to Miss Hayden instead. When Gillian hears about this provision of his uncle's will, he immediately pretends that he lost all the money at the racetrack, and so is not entitled to his share of the estate.
The problem for Gillian is that he just didn't know what to do with all that money. And that was only $1,000, a relatively small amount. He must've thought how much worse it would've been for him to have $50,000 instead, and all the additional problems that would've created. Gillian has learned that sometimes money can be a burden, whether it's too much or not enough. And as the story closes, Gillian's merry whistling convinces us that he's glad to be relieved of it.