The Missing $1

If you’ve read a few math books you’ve undoubtedly come across this one before, but if you haven’t … it’s an awesomely confusing paradoxical conundrum possessing the possible property of stumping anyone, regardless of his level of mathematical ability. 

It goes something like this:

Fifty or sixty years ago, three salesmen traveling through the Rocky Mountains pull up to a motel late one stormy, snowy night.  They’re tired, hungry, and in desperate need of shelter.  The proprietor hesitates but can’t turn them away, so he rents them the only room available for $30.  They pull out their wallets and each forks over a $10 bill.  They take the key, grab their luggage, and find the room. 

Which is a complete mess.  Beds undone, dirty towels on the floor, you name it.  It’s filthy.  They ring up the proprietor who admits he knew the room was a mess.  Something about being shorthanded and having too much to do to prepare for the storm and whatnot.  He offers to shave $5 off the bill as a goodwill gesture.  The salesmen agree and the proprietor sends his son out in the blizzard with five singles to return to his guests.

The men decide to each take a dollar back, and tip the young lad the remaining $2 for his trouble.

Now, let me ask you a question.

Each of the three traveling salesmen effectively paid $9 for the room ($10 less the $1 refund).  That’s $27 from the trio.  And they tipped the proprietor’s son $2.  So … $27 + $2 = $29.

What happened to the other dollar?

Hmm?