Before reading the answer can I interest you in a clue?
possibly wont be surprised to hear that there is no missing dollar. It
adds up just fine. In trying to explain this I've always
thought it was helpful to consider the puzzle with some different
numbers in it. (Equally it may not be helpful, you could skip to the end.) Consider this....
men go into a hotel.
The man behind the desk said the room is $3000 so each man paid $1000
and went to the room.
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
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
at this point you would never ask:
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?
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.
the short answer:
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