One of my favourite puzzles is this one, from the 1930s:

Three people check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later the clerk realises the bill should only be $25.

To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realises that he cannot divide the money equally. As the guests didn’t know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 as a tip for himself.

Each guest got $1 back, so now each guest only paid $9, bringing the total paid to $27. The bellhop has $2. And $27 + $2 = $29 so, if the guests originally handed over $30, what happened to the remaining $1?

Try to solve this without any further hints.

Obviously, there’s a trick.

The misdirection in this riddle is at the end of the description, where a bunch of unrelated numbers are added together – only to misguide the listener.

There’s no reason to add these random totals, and even less reason for the sum to add 30. If you wanted to sum up the cash total, you have to look at the $25 in the register, the 3*$1 in the guests’ pocket, and the $2 with the bellhop. That’s, as expected $30.

More missing dollars on Wikipedia.