# Answer to Riddle #28: Hotel Room, Bellboy and the Missing Dollar

28. 3 men go into a hotel. The man behind the desk says a room is $30 so each man pays $10 and goes to the room.

A while later the man behind the desk realized the room was only $25 so he sent the bellboy to the 3 guys' room with $5. On the way the bellboy couldn't figure out how to split $5 evenly between 3 men, so he gave each man a $1 and kept the other $2 for himself.

This meant that the 3 men each paid $9 for the room, which is a total of $27 add the $2 that the bellboy kept = $29. Where is the other dollar?

A while later the man behind the desk realized the room was only $25 so he sent the bellboy to the 3 guys' room with $5. On the way the bellboy couldn't figure out how to split $5 evenly between 3 men, so he gave each man a $1 and kept the other $2 for himself.

This meant that the 3 men each paid $9 for the room, which is a total of $27 add the $2 that the bellboy kept = $29. Where is the other dollar?

This puzzle gets e-mailed to me all the time and I don't really like it because it's less of a lateral thinking riddle than a bit of a trick. Plus I've always struggled to find a good way of explaining it...

Before reading the answer can I interest you in a clue?

You possibly wont be surprised to hear that there is no missing dollar. It adds up just fine. I have two ways of thinking about this for you:

Put another way consider how the $30 breaks down:

You possibly wont be surprised to hear that there is no missing dollar. It adds up just fine. I have two ways of thinking about this for you:

## The short answer:

There is no missing dollar. The men spent $27. Of which $25 went on the room and $2 went to the light fingered bell boy. You can not add the $2 the bellboy has to the $27 the men spent as this $2 actually comes out of the $27 the men spent, the other $25 going on the room.Put another way consider how the $30 breaks down:

- $25 — room
- $3 (3x $1) — back to the men
- $2 — Bellboy

## The long answer

In trying to explain this I've always thought it was helpful to consider the puzzle with some different numbers in it. (You may not, but we'll see.) Consider this....3 men go into a hotel. The man behind the desk says a room is $3000 so each man pays $1000 and goes to the room.Now at this point you would never ask:

A while later the man behind the desk realized the room was only $25 (he's that stupid,) so he sent the bellboy to the 3 guys' room with $2975. On the way the bellboy couldn't figure out how to split $2975 evenly between 3 men, so he gave each man a $991 and kept the other $2 for himself.

This meant that the 3 men each paid $9 for the room, which is a total of $27 add the $2 that the bellboy kept = $29. Where is the other $2971?Remember this puzzle is exactly the same. It's just the numbers from the first puzzle are confusing (to me anyway.) In this we know there is no missing $2971 because we saw where all that money went. By making this number larger we can see it moving, we can see that it was mostly shared by the three men. In the real puzzle there are several small amounts bobbing about and they're harder to track. But the answer is the same, there is no more a missing dollar than there was a missing $2971.

© Nigel Coldwell 2004 - – The

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