The missing dollar.

Posted by Les on Thursday, August 01, 2002 at 04:38 PM. Read 10217 times. Tags:
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I got an old riddle in an email today that’s always been a stumper for a lot of folks. It pops up about once every other year in my inbox and I managed to work out the answer years ago, but it’s still amusing to see that folks are still struggling with it. Different variations on it pop up from time to time, but the basic gist of it is always the same. This latest one reads like this:

Three men go into a motel. The desk clerk said the room was $30, so each man pays $10 and goes to their room. A while later, the desk clerk realizes the room was only $25, so he sends the bellboy to the 3 guys’ room with $5. On the way, the bellboy can’t figure out how to split $5 evenly between 3 men, so he gives each man $1 and keeps the other $2 for himself. This means that the 3 men each paid $9 for the room, which is a total of $27. Add to that the $2 the bellboy kept and the total is $29.

Where is the other dollar?

I know the answer to this one, but I’ll wait before posting it in case folks wanna take a crack at it.

Updated: Here’s the solution:

The answer is: There is no other dollar.

The math isn’t wrong here, the instructions are wrong. Think of the problem this way:

At the end of the day, each man has put in $9 towards the cost of the room: 3 x $9 = $27.
The bellboy has kept $2 from what the men spent for himself: $27 - $2 = $25.
The motel has collected $25.

Or to take it from the other direction:

The motel has $30 and gives $5 of that to the bellboy to return to the men: $30 - $5 = $25.
The bellboy, not knowing how to split $5 equally decides to keep $2 for himself: $5 - $2 = $3.
The men each end up with $1 each. Total it up: 3 x $1 + $2 + $25 = $30.

About the best the bellhop could have done would be to give two men $1.67 and the last $1.66, which would be about as close to evenly dividing $5 he could have come to. The mistake in the instructions is when the riddle asks you to “add the $2 the bellboy kept” to the total the men spent. The bellboy took that money from the total so you would subtract it, not add it. Now, how many of you are slapping your foreheads right about now? 

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KPatrickGlover United States Posted on 10/01/2006 at 12:26 AM

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Maid. Never seen a post office open on a sunday.

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LuckyJohn19 Australia Posted on 10/01/2006 at 02:55 AM

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KPG: Maid. Never seen a post office open on a sunday.

I’d never have thought of that.
I often used to collect my mail on Sundays from my post office box.  wink

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I’ve discovered that it all boils down to brain wiring: your brain is wired to worship magic or it isn’t, either it’s wired to utilize logic or it isn’t, either it’s analytical of myths or it isn’t.

Les United States Posted on 10/01/2006 at 11:06 AM

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Depends on where you are, KPG. Sunday Mail Delivery was common at the start of this country and is still the norm in several places around the country. See this entry about Sunday Mail Service in a Christian Nation over at atheism.about.com.

Of course that’s just me being nitpicky and probably has nothing to do with the riddle.

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KPatrickGlover United States Posted on 10/01/2006 at 11:17 AM

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Ha!

I stand corrected but stand by my answer as well.

The only reason for specifying that the murder took place on a Sunday afternoon is that being Sunday is significant. The postal delivery is the only one that seems to be contradictory to that.

I wish our post office here was open on Sundays.

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coolaxman94 United States Posted on 01/09/2007 at 09:25 PM

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I got a good riddle
An adventurer is walking through the forest when he is caught and drugged by cannibals.  When he comes to they tell him he may make one statement.  If it’s true they’ll boil him in water if it’s false they’ll fry him in oil.  He makes his statement and is set free.  How is this possible?

LuckyJohn19 Australia Posted on 01/10/2007 at 03:31 AM

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The maid - cos there’s no mail on Sundays.
Having said that - one can collect the mail from the Post Office BOX, with a key, any day.

From memory KPG exposed this one some time ago.
I’m a bubble-burster from way back.  LOL

LuckyJohn19 Australia Posted on 01/10/2007 at 03:53 AM

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FUCK this!!!
I’m not gonna play here anymore whilst there’s this Page 1, 2, etc bullshit.

No redface but I’m LOL

coolaxman94 - maybe the silly bastard woke up from a dream and realised too much dope can fry your brain. I know abitaboutit. wink

Anonymous United States Posted on 04/07/2007 at 10:23 PM

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You’ll boil me in oil is the statement.

If they do boil in oil, then the statement is true, so they should have boiled in water.

If they boil in water, then the statement, is then false, so they should boil in oil.

Ryan Peterson United States Posted on 06/29/2007 at 11:26 PM

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You can work it backwards all you want. This is a famous (and rare) case of algebra failing us. The thing is, there were $30 at the beginning. At the end, there are $29. The three men spent a total of $27. The bellboy kept $2. The hotel has $25 and gave up $5. There is a missing $1.

Les United States Posted on 06/29/2007 at 11:44 PM

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No Ryan, there isn’t a missing $1. The solution was provided earlier on in the comments. It all adds up correctly.

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All I know is the wine lasts longer when you don’t gotta share it with someone
All I know is my steak tastes better when I take my steak tastes better pill
-- I Feel Fantastic, Jonathan Coulton

elwedriddsche United States Posted on 06/30/2007 at 01:11 AM

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Ryan, algebra is never wrong—as opposed to your understanding of it wink

What happens is that 3*(10-1) = 25 + 2

Each guy spent $9, of which $25 go to the hotel and $2 to the bellboy.

Or if you look at it differently, 30 = 25 + 2 + 3*1

Of the $30 the guys originally spent, 25 go to the hotel, 2 to the bellboy, and 1 goes back to each of the guys.

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Philosophy is questions that may never be answered.
Religion is answers that must never be questioned.
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zilch Austria Posted on 06/30/2007 at 02:55 AM

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Sorry, guys, Ryan is right.  The leprechauns got the missing dollar.

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elwedriddsche United States Posted on 06/30/2007 at 11:27 AM

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Zilch, don’t make me revoke your blackboard privileges.

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Science is answers that must always be questioned.
Philosophy is questions that may never be answered.
Religion is answers that must never be questioned.
Politics is answers that lobbyists pay for.

coolaxman94 United States Posted on 07/05/2007 at 10:28 PM

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here’s a hard riddle

A logician with some time to kill in a small town decided to get a haircut. The town had only two barbers, each with his own shop. The logician glanced into one shop and saw that it was extremely untidy. The barber needed a shave, his clothes were unkempt, his hair was badly cut. The other shop was extremely neat. The barber was freshly shaved and spotlessly dressed, his hair neatly trimmed. Why did the logician return to the first shop for his haircut?

elwedriddsche United States Posted on 07/05/2007 at 10:49 PM

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Because each barber trimmed the other’s hair?

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Science is answers that must always be questioned.
Philosophy is questions that may never be answered.
Religion is answers that must never be questioned.
Politics is answers that lobbyists pay for.

Julian India Posted on 07/06/2007 at 02:23 AM

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Plus its easier to keep your surroundings and self neat if have a lot of free time. The first barber was kept busy by the townsfolk who probably knew from experience who the better barber was.

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zilch Austria Posted on 07/06/2007 at 03:31 AM

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Not only that, but the first barber was obviously the one who shaved everyone in town who didn’t shave himself, and rather than participate in the old paradox, he simply went without shaving.

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You were born.  And so you’re free.  So happy birthday.
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coolaxman94 United States Posted on 07/12/2007 at 06:04 PM

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dang u guys r too good
i’ve still got sum more

1. what comes once in a minute twice in a moment but never in a thousand years?

2.I can be long, or I can be short.
I can be grown, and I can be bought.
I can be painted, or left bare.
I can be round, or square.
What am I?

3. I never was, am always to be, no one ever saw me, nor ever will. And yet I am the confidence of all to live and breathe on the terrestrial ball. What am I?
There once was a strange man who loved wordplay, he had a very important sucessful busisness that would take insect shipments from all across the world and distribute them to zoos all across the US.

What is the name of his company?

clues
1. the anwser is 9 letters

2. i have left some important clues and not so important clues in both versions

3. i have allready told you the anwser

4. remember it has to do with wordplay
4.

Marko United States Posted on 10/19/2007 at 05:45 PM

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The maid...no mail on sundays.

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