Wednesday, November 12, 2008

The missing dollar..

I am going to lighten up a bait and post an old math puzzle that no one has ever been able to explain to me why it doesn't add up.

3 guys are going on a hunting trip and each pitch in $10 on a hotel room. They pay the desk clerk, get the key and go to the room to get some sleep for an early morning adventure. The clerk's boss shows up and tells the clerk he had promised the room to the hunters for $25. He gives the clerk $5 in one dollar bills and tells him to take it to the hunter's room and refund them the $5. The hunters are so happy with the honesty of the hotel, they each accept a $1 bill and tip the clerk $2 for his trouble.
So each hunter has now paid $9 a piece for their room for a total of $27. Add that back to the $2 the clerk got for a tip and you only come up with $29. What happened to the missing $1?


One Reader said...

Ok, but they didn't each pay $9 for their room - the room only cost $25, so two paid $8.33 and one paid $8.34, adding up to $25. If they paid $8.33 (or $8.34) & got $1 back that means two of them tipped $.67 and one tipped $.66 adding up to the $2. Or something like that. ;-)

dkelly said...


I'm not sure I understand what One Reader means, but the apparent difficulty is that the wrong things are being added--I'm reminded of a New Yorker cartoon of a road sign "Welcome to Pilleywog, Founded 1729, population 10000, elevation 289, total: 12018".

Here are two correct ways of looking at it. Consider the $30;
the desk clerk has 25, the men collectively have 3, and the bellhop has 2--so the total is $30.

You can also look at it person-by-person: The desk clerk has $25, the men collectively have -$27 (that's negative), and the bellhop has $2--so the sum is 0 which is what it was before the start of the story.

I like to preface the story with a different version, a set-up for the con--adding up the same wrong things, but rigging it so that the sum seems correct: Same $30, but the desk clerk gives the bellhop $6 to return; the bellhop returns 3 and keeps 3--now the men are out collectively $27 and the bellhop has $3, so the total is $30, as (should not have been) expected.

Someone wrote a poem about this story I'd be happy to have a reference for.

Be Well,