The missing dollar.

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?

48 thoughts on “The missing dollar.

  1. 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?

  2. 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

  3. 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

  4. 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

  5. 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 $31.  muahahahaha and there is your missing 1$

  6. 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.

  7. 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

  8. 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

  9. 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)

  10. 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.

  11. 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?

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

  13. 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

  14. 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

  15. 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.

  16. 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.

  17. 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?

  18. 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

  19. 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

  20. 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.

  21. 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.

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

  23. 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.

  24. 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?

  25. 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.

  26. 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.

  27. 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.

  28. The answer to number one is: (1. what comes once in a minute twice in a moment but never in a thousand years?)

    the letter “M”

  29. At first, i thought nubmer 2 was hair but then i read along where it says “round and square” so it has to be fingernail.

    Number 3 i know the answer to but i will not say since i don’t agree with it.

    Number 4 is either The Zoo or Wordplay

  30. ok to get it right there is not a dollar missing there is a penny missing. cuz 25/3=8.33+1.00=9.33*3=27.99+2.00=29.99
    $25 being how much they all paid forthe room so devide it by 3 wich is 8.33 plus the $1 they got back is $9.33 then multiply it by the 3 guys is $27.99 then add the $2 the bell boy has that makes $29.99

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