The Missing Dollar

Lee Baucum · From: McAllen, Texas (Extreme South) The Final Frontier

Three men go to stay at a motel, and the man at the desk charges them $30.00 for a room. They split the cost ten dollars each. Later the manager tells the desk man that he overcharged the men, that the actual cost should have been $25.00. The manager gives the bellboy $5.00 and tells him to give it to the men.

The bellboy, however, decides to cheat the men and pockets $2.00, giving each of the men only one dollar.

Now each man has paid $9.00 to stay in the room and 3 x $9.00 = $27.00. The bellboy has pocketed $2.00. $27.00 + $2.00 = $29.00 - so where is the missing $1.00?

Sandy Inglis · From: Christchurch New Zealand

The men paid $30 - $3 = $27
The room cost $25 / 3 = $8.33333 each
The Bell Boy pocketed $2
The difference is $0.33333 * 3 = $1?
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Bruce Blackburn · From: Nashville, Tennessee

They didn’t pay 27 a piece. They paid 25/3 a piece
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Fred · From: Amesbury, MA

The men ended up paying out $27. The motel got $25 and the bellboy got $2 adding up to $27. There’s no missing dollar.

Chase Brady · From: Ohio, USA

Problems like this hinge on a bit of verbal sleight of hand -- making something sound reasonable when it's not. The trick here is the statement "$27.00 + $2.00 = $29.00". The $2 the bellboy pocketed is actually part of the $27 paid. Adding them together gives you a meaningless sum. There's no reason it should add up to $30. (Sorry, I used to teach Freshman math.)

Jeff Garden · From: Center Sandwich, New Hampshire, USA

I remember this scene from the movie Paper Moon with Ryan and Tatum O'Neal about a con man and a clerk making change. I'll admit to never being the brightest bulb in the circuit - it left me thinking "what just happened? how did he do that?"
https://www.youtube.com/watch?v=60ePD3hg73g

Bill Sinclair · From: Hagerstown, Maryland, USA

This same "problem" is used in the opening chapter of Jim Al-Khalili's book Paradox - The Nine Greatest Enigmas in Physics as an example of a falsidical paradox. No, it's not among the nine, but a good example of how easy it is to direct someone to the wrong conclusion by inserting false or unrelated factors into the equation. Verbal slight of hand is a great way to put it, Chase.

I'm not the brightest bulb either, Jeff, but that was a fun trip down memory lane. "That just don't seem quite right - somehow" could be easily be my motto.

Larry Mingua · From: Indiana, USA

SLOW DAY IN TEXAS

It's a slow day in a little East Texas town. The sun is beating down, and the streets are deserted.

Times are tough, everybody is in debt, and everybody lives on

credit.....

On this particular day a rich tourist from back East is driving

through town. He stops at the motel and lays a $100 bill on the desk

saying he wants to inspect the rooms upstairs in order to pick one to

spend the night.

As soon as the man walks upstairs, the owner grabs the bill and

runs next door to pay his debt to the butcher.

The butcher takes the $100 and runs down the street to retire

his debt to the pig farmer.

The pig farmer takes the $100 and heads off to pay his bill at

the supplier of feed and fuel.

The guy at the Farmer's Co-op takes the $100 and runs to pay his

debt to the local prostitute, who has also been facing hard times and has

had to offer her "services" on credit.

The hooker rushes to the hotel and pays off her room bill with

the hotel owner.

The hotel proprietor then places the $100 back on the counter so

the rich traveler will not suspect anything.

At that moment the traveler comes down the stairs, picks up the

$100 bill, states that the rooms are not satisfactory, pockets the money,

and leaves town.

No one produced anything. No one earned anything.

However, the whole town is now out of debt and now looks to the future with a lot more optimism.

Jeff Garden · From: Center Sandwich, New Hampshire, USA

Whoa, I'll say it again..what just happened?!

Doug Beaumier · From: Northampton, MA

These riddles remind my of the Lonzo and Oscar song "I'm My Own Grandpa".

Now, many many years ago
When I was twenty three
I was married to a widow
Who was pretty as could be

This widow had a grown-up daughter
Had hair of red
My father fell in love with her
And soon the two were wed

This made my dad my son-in-law
And changed my very life
My daughter was my mother
'Cause she was my father's wife

To complicate the matters
Even though it brought me joy
I soon became the father
Of a bouncing baby boy

My little baby then became
A brother-in-law to dad
And so became my uncle
Though it made me very sad

For if he was my uncle
That also made him the brother
Of the widow's grown-up daughter
Who, of course, was my step-mother

I'm my own grandpa
I'm my own grandpa
It sounds funny I know
But it really is so
I'm my own grandpa

My father's wife then had a son
That kept them on the run
And he became my grandchild
For he was my daughter's son

My wife is now my mother's mother
And it makes me blue
Because, she is my wife
She's my grandmother too

I'm my own grandpa
I'm my own grandpa
It sounds funny I know
But it really is so
I'm my own grandpa

Now, if my wife is my grandmother
Then, I am her grandchild
And every time I think of it
It nearly drives me wild

For now I have become
The strangest case you ever saw
As husband of my grandmother
I am my own grandpa

I'm my own grandpa
I'm my own grandpa
It sounds funny I know
But it really is so
I'm my own grandpa
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