A couple of weeks ago, this old riddle came up in conversation with a group of friends from my church. It’s a good riddle, and an old one – you can easily find discussions of the problem and solution online (but don’t cheat):

Three guests check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later the clerk realizes 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 realizes that he cannot divide the money equally. As the guests didnt know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 for himself.

Now that the guests have been given $1 back, each has paid $9, bringing the total paid to $27. The bellhop has $2. If the guests originally handed over $30, what happened to the remaining $1?

Can you explain?

I was prompted to revisit this as I thumbed through a book I found laying around the house. The version in this book has a couple of interesting differences. It starts with three men asking for three separate rooms for thirty dollars. The clerk realizes that the rooms should have been $25. That got my goat – $25 for three rooms? So, the hotel has a three-for-twenty-five deal? A sale price of $8.33 for a room? All, I suspect, to avoid speculation about the three men sharing a room.

I found this updated version of the same riddle. This one bypasses most of the difficulties of the traditional version:

The Waiter

Three men in a cafe order a meal the total cost of which is $15. They each contribute $5. The waiter takes the money to the chef who recognizes the three as friends and asks the waiter to return $5 to the men.

The waiter is not only poor at mathematics but dishonest and instead of going to the trouble of splitting the $5 between the three he simply gives them $1 each and pockets the remaining $2 for himself.

Now, each of the men effectively paid $4, the total paid is therefore $12. Add the $2 in the waiters pocket and this comes to $14…..where has the other $1 gone from the original $15?