April 1, 2002
Problem of the Week
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 to the Problem:
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:
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1. Joshbeen Grewal
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College of William and Mary, Williamsburg, Virginia
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| 2. Keith Mealy
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Cincinnati, Ohio
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| 3. David Powell
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Winchester, Virginia
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| 4. George Gaither
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Winchester, Virginia
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| 5. Brice Tarleton
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Columbus, Georgia
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| 6. Richard Johnson
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La Jolla, California
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| 7. Walt Arrison
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Philadelphia, Pennsylvania
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| 8. Renata Sommerville
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Austin, Texas
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| 9. Nate Troup
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Arlington, Virginia
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| 10. Andrea Flandry
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Columbus, Georgia
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| 11. Kristen Wilson
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Columbus, Georgia
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| 12. Adam Kronfeld
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Bucknell University, Lewisburg, Pennsylvania
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| 13. Christopher March
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Virginia Tech, Blacksburg, Virginia
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| 14. Theresa Gipson
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Rockford, Michigan
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| 15. Amy Lamport
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Rockford, Michigan
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