Dividing the Cost of a Hotel Room

Date: 11/20/95 at 13:20:17
From: Anonymous
Subject: math

Three men walk into a hotel. One room costs $30. Each man only 
has ten dollars. They rent one room and get a rollaway bed.  

Later that night the clerk remembers that he forgot to subtract 
the five dollar discount. He takes five ones back up to the men.  
He doesn't know how to split five dollars between 3 people so he 
keeps two dollars and gives the men one dollar each.  

Now each man has only paid 9 dollars.  If each man paid nine 
dollars and the clerk kept 2 it doesn't add up. (9*3=27+2=29) 

Where did the extra dollar go?

Date: 11/20/95 at 15:57:4
From: Doctor Ethan
Subject: Re: math

Ah what a great question,

When I was in the sixth grade I was told this story and I 
almost cried because I couldn't figure it out. I was in 
torment.  I did eventually figure it out, but it was painful.

So instead of just telling you the answer I will give you a few 
questions to answer. Let's start with a few facts.

There are thirty total dollars to be accounted for.
The men are out 9 dollars apiece, for a total of 27.

  1. Who got the 27 dollars? (two people)
  2. If we were to divide the money into two categories and the 
     first was MONEY SPENT, what would the second be?
  3. To retrieve the total, why are 27 and 2 the wrong numbers?

Good luck with this.

-Doctor Ethan,  The Geometry Forum

Date: 03/07/97 at 13:18:01
From: Doctor Rob
Subject: Re: Brain teaser

I love this old chestnut!

Answer: Since each man has now paid $9 for the room (3 x 9 = 27), 
and the clerk has $2 in his pocket (27 - 2 = 25), the rest of 
the money is in the hotel till.

The trick is to realize that the $2 has to be subtracted from 
the $27, not added to it.

-Doctor Rob,  The Math Forum
 Check out our web site! http://mathforum.org/dr.math/