Riddle: "The case of the missing dollar"

[Barad Simith]

(This is an oldie, but more often than not I find the listener has never heard it.)



Three men are traveling, and they're short of money so they've been sleeping outside.

But one night, the weather is so bad they realize they'll likely die of exposure if they don't find shelter. They decide to get a hotel room, even if it means spending the last of their money.

They find a hotel and ask the employee at the desk how much a room for three costs. He tells them it's $30 a night, so they each give him $10.

After the men have gone upstairs to their room, the manager comes out from the back. He's heard everything, and is angry with the clerk.

"You know as well as I do that a room for three costs $25!" he tells the clerk. The clerk was clearly going to pocket the extra five.

The manager takes five $1 bills from the cash drawer and gives them to the clerk, then orders him to go upstairs and give the men their money back.

So the clerk knocks on their door and gives them the five $1 bills, explaining: "I'm sorry, but I'm new here, and I was mistaken about the cost of your room. It's actually $25. Here's your $5 refund."

The men explain to the clerk that it would be hard to divide five $1 bills between the three of them, so they each take $1, and let them clerk keep $2 ("as a tip, for being so honest").

Now each of the men has paid $9 for his share of the room, instead of $10. (They initially paid $10 each, but having received a $1 refund, they have now each paid $9.)

$9 times three is $27. And they tipped the clerk $2, so the total amount paid is $29.

What happened to the missing dollar?

[Barad Simith]

1. BTW, I once told this to a drunk in a bar, and after an hour he said:

"The manager took it!"

[maveric]

2. This riddle caused a fistfight at the shipyard I worked at.

Out of frustration and taunting.

[TiredTexan]

3. This happens when you mix up

arithmetic and geometric progressions in the same problem. You have to start with the $30 amount, which is derived by adding (not multiplying) the three 10 bills. You then subtract the $2 given the clerk, and this is what each paid for the room. The men paid 1/3 of $28 (or 9.33) each for the room (less the .666666 each paid to the clerk for the tip), not $9.00 each for the room.

[diddlysquat]

4. Try this:

The $2.00 tip is included in the $27.00. $25.00 plus $2.00 tip. Then each man took back $1.00. $27 + 3 (returned and KEPT by the three men) = $30.00

[Barad Simith]

5. That's probably the clearest explanation I've seen...

...even though TiredTexan's was also correct.

They paid $9 each, totaling $27. The $2 tip is subtracted, not added.