Riddle of the Week

Riddle of the Week: The Missing Dollar

Difficulty level: Moderate

 
By Jay Bennett

We have a classic riddle for you this week, one that dates back to the 1930s at least, and the concept is older still. The math is simple and straightforward on this one. Until it's not.

PROBLEM

Three people check into a hotel. The clerk tells them that the bill for their stay is $30, so each person pays the clerk $10. The clerk puts the money in the cash register.

Later that night, the clerk realizes that he made a mistake and should have only charged the three guests $25. He pulls $5 in one dollar bills out of the register and tells the bellhop to return the money to the guests.

On the way to the room, the bellhop realizes that he cannot split the money evenly between the three people. As the guests don't know that they were charged the incorrect amount for their room, the bellhop decides to simply give them $1 each and pocket the extra $2 as a tip. Each guest gets $1 back, so they each paid $9 for their room, totaling $27. The bellhop kept $2, and $27 + $2 = $29.

But the guests originally handed over $30. What happened to the missing dollar?

HINT

What would this problem look like if the clerk decided to refund the guests for $10 instead of $5? What about $20?