Answer to April 1, 2002 Problem

The Bellman Problem

Three people went to a hotel and rented a room for $30, each paying $10 for his share. Later, the clerk discovered that the price of the room was only $25. She handed the bellman five $1 bills and asked him to return them to the three people. The bellman, not knowing how to divide $5 among three people, instead gave each person $1 and kept the other $2 for himself.

Here's the question:
The three people originally paid $10 each, but each received $1 back, so they've now paid a total of $27 for the room.
Add to that the $2 that the bellman kept, and you have a total expenditure of $29 instead of $30. What happened to the other dollar?

Solution:

There is no missing dollar.
This is a classic problem -- it has been around for at least 30 years.


The total expenditure is now only $27, accounted for by adding the $25 in the hands of the hotel clerk to the $2 in the hands of the bellman.
In other words, the original $30 now is divided like this:
the hotel clerk has $25, the guests have $3, and the bellman has $2.

The error arose when an asset ($2) was added to an expense ($27) instead of the other asset ($25), thereby "mixing apples with oranges."


Correctly solved by:

1. Joshbeen Grewal College of William and Mary, Williamsburg, Virginia
2. Keith Mealy Cincinnati, Ohio
3. David Powell Winchester, Virginia
4. George Gaither Winchester, Virginia
5. Brice Tarleton Columbus, Georgia
6. Richard Johnson La Jolla, California
7. Walt Arrison Philadelphia, Pennsylvania
8. Renata Sommerville Austin, Texas
9. Nate Troup Arlington, Virginia
10. Andrea Flandry Columbus, Georgia
11. Kristen Wilson Columbus, Georgia
12. Adam Kronfeld Bucknell University, Lewisburg, Pennsylvania
13. Christopher March Virginia Tech, Blacksburg, Virginia
14. Theresa Gipson Rockford, Michigan
15. Amy Lamport Rockford, Michigan