The missing dollar.

Posted by Les on Thursday, August 01, 2002 at 04:38 PM. Read 9108 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? 

Comments:

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Ashley United States Posted on 11/01/2002 at 12:24 PM

Ashley pic

I would like to know the answer to this.

Les United States Posted on 11/03/2002 at 10:47 AM

Les pic

Ask and you shall receive. grin

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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When one reads Bibles, one is less surprised at what the Deity knows than at what He doesn’t know.
-- Mark Twain

United Kingdom Posted on 02/10/2003 at 06:49 PM

 pic

the manager then said it was $25 so he gave the bell boy $5 to take back to the men! dont forget brit the man still has the $25 in the till, so the bell boy went to the room and give them all a doller each so that means they did pay $9 each thats true but including the $25 in the till plus the $3 the men got back which equals $28 , then it says the bell boy kept $2 of the $5 returned

so $25 behind the counter alreayd piaded for plus the $3 the man got back plus the $2 the bell boy kept = $30 !!!!!!!! so there is no missing doller !! its all there

Shaun Hillier United Kingdom Posted on 03/11/2003 at 05:34 AM

Shaun Hillier pic

THe answer is that the room doesnt cost $27 it cost $25 so the bell boy took $2 and they get $3 back so if you add it all up it should add up to $30

Les United States Posted on 03/11/2003 at 08:46 AM

Les pic

I love it when people post the answer repeatedly after I’ve already posted it. Amazing.

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When one reads Bibles, one is less surprised at what the Deity knows than at what He doesn’t know.
-- Mark Twain

JoeY United States Posted on 07/16/2003 at 01:09 PM

JoeY pic

25/3 8.33 add a dollar because he gave him a dollar each 9.33 x 3 = 28 + the 2 dollars from the bellboy

Walldog United States Posted on 10/03/2003 at 07:12 PM

Walldog pic

The following night two friends check into the same motel. Once again the clerk charges them $30, that is $15 per person. After the clerk remembers the price rate is only $25 he sends the bellhop upstairs with five $1 bills to pay the two friend’s back. The bellhop knows he got away with it once so he tries it again. But this time he pockets $3 and returns $2 to the hotel guests ($1 per guest). So each of the two guests got $1 back from their original $15. Therefore each paid $14 which is a total payment of $28 for the room. Now the bellhop has $3, the guests paid $28, for a total of $31.  muahahahaha and there is your missing 1$

Greg New Zealand (Aotearoa) Posted on 10/27/2003 at 02:18 AM

Greg pic

Walldog, that is probably THE best explanation I have heard for that riddle.  Top draw!!

ksm United States Posted on 11/20/2003 at 09:09 PM

ksm pic

The math is incorrect.  You cannot add the Bellboy’s $2 to the guests’ $27 because the $2 is part of what the guests spent their $27 on for the hotel.  $25 went to the hotel and $2 went to the Bellhop.

Bobby South Africa Posted on 01/08/2004 at 12:59 PM

Bobby pic

I just want to know why 3 men only got 1 room?

Tish Australia Posted on 01/08/2004 at 02:43 PM

Tish pic

Bobby, They were conjoined triplets… :evillaugh:

segal Trinidad and Tobago Posted on 01/17/2004 at 06:45 AM

segal pic

The following night one of the two friends check into the same motel. Once again the clerk charges him $30, that is $30 per person. After the stupid clerk remembers the price rate is only $25 he sends the bellhop upstairs with five $1 bills to pay the guy back. The bellhop knows he got away with it twice so he tries it again. But this time he pockets $4 and returns $1 to the hotel guest. So the guy paid $29 plus $4 the bellboy pockets which is a total pament of $33 for the room.

You have two more...........

Thanks Walldog, It makes we see how incorrect the calculates are grin

andy United States Posted on 04/26/2004 at 08:55 PM

andy pic

so wait if the doller wasnt missing and the people didnt gett jipped why make the riddle orrrrr what if one of them had a beer witch cost a doller but it was a super large beer and he was so pisssed he forgot to mention it in the riddle therefore the missin doller is beer money

dun worrie i do get it just thorght id be creative

Me United States Posted on 05/01/2004 at 02:54 PM

Me pic

you are right Les..it is amazing! LOL

Just passing through United States Posted on 07/31/2004 at 01:55 AM

Just passing through pic

This is one of those times I wish I was any good at math...>.<

t-virus United States Posted on 09/07/2004 at 06:31 PM

t-virus pic

he is a riddle 2 guys are in the bar one says he can drink so quickly that no one can beat him no matter what.  So the guy on the right says hey i bet i can drink these two humongus glasses before you can drink that small little tiny shot glass. With your choice of the drink.  The guy on the left says sure but, he knows there must be a trick so he says okay let me choose the rules.  The guy on the right says okay but, since you choose the rules i get to drink one of my glasses before and put it down before you can drink.  Guy on the left says okay the rules are we can not touch each others glass with an object, spit in the glass or do anything to the other players glass with anything.  The guy on the left thinks he just won now the guy on the right can’t spit or do anything to his drink. But yet the guy on the right wins how is that possible.  (Great way to make money)

t-virus United States Posted on 09/07/2004 at 06:34 PM

t-virus pic

might tell you
oh also i ment to say here not he.
Also is someone already wrote this riddle or if i am doing something wrong sorry.

deadscot United States Posted on 09/07/2004 at 09:07 PM

deadscot pic

After the first guy finishes his first drink he sets his glass down on top of the other guy’s shot glass.

My turn -

You must choose between two cylinders.  They are identical in size and appearance.  Each is painted green.  One is solid and made out of a non-magnetic alloy, while the other is hollow and made of gold.  They both have the same measurements and density.  You are not allowed to scratch through the paint or strike the objects in any way.  You have absolutely no external devices.  What is the simplest way to determine which cylinder is made of gold?

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To know a person’s religion we need not listen to his profession of faith but must find his brand of intolerance. - Eric Hoffer

Les United States Posted on 09/07/2004 at 09:20 PM

Les pic

Roll them across the floor. The hollow cylinder will travel farther than the solid one.

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When one reads Bibles, one is less surprised at what the Deity knows than at what He doesn’t know.
-- Mark Twain

t-virus United States Posted on 09/15/2004 at 04:05 PM

t-virus pic

everyone is way to smart here

t-virus United States Posted on 09/15/2004 at 04:10 PM

t-virus pic

mark my words i will figure out a riddle no one can solve

t-virus United States Posted on 09/29/2004 at 09:26 PM

t-virus pic

I need help finding the nth term i mean you guys are smart you can help me

Bob United States Posted on 10/01/2004 at 12:08 AM

Bob pic

Here’s a non-math one.

The man who made it didn’t want it.
The man who bought it didn’t need it.
The man who used it didn’t know it.
What is it?

Answer to the Question

deadscot United States Posted on 10/01/2004 at 08:46 AM

deadscot pic

So many political insinuations could be made on this one.  The real answer is of course a coffin.

coolaxman94 United States Posted on 09/30/2006 at 06:28 PM

coolaxman94 pic

ive got one.
a rich billionaire is killed on sunday afternoon.the police come and investigate but all of the suspects have an alibi for the ETOD
Gardener-buying mulch
Cook-making lunch
Maid-getting mail
Wife-walking dog
Daughter-helping at church
personal trainer-lifting weights
(every room has a camera)
based on this info who is the killer

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