The Mystery of the Missing Dollar: Can You Solve It?

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SUMMARY

The discussion centers around the classic riddle known as "The Mystery of the Missing Dollar," which illustrates a common mathematical fallacy. Three individuals pay $30 for a hotel room, but after a refund of $5 from the desk clerk, the bellhop retains $2 and returns $3 to the guests. This leads to the misleading calculation of $27 plus $2 equating to $29, creating confusion over the missing dollar. The resolution emphasizes that there is no missing dollar; the error lies in the misrepresentation of the total costs involved.

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ProfessorLogical
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it's not all that sophisticated but it has given a hard time even to some math people.

3 people on a trip go to a hotel to get a room to spend the night in.

the desk clerk just happens to not be there, so the bellhop says can take care of you but I'm not sure how much a room cost, i think it's $30. so they pay him $30...$10 each.

the desk clerk comes back and the bellhop tells him what happened. he tell the bellhop he overcharged the people. he gives the bellhop $5 and tells him to go to their room and return the money.

on the way to the room the bellhop figures they'll never know, so he decides to keep $2 for himself and only give them back $3. so he gets to their room, tells them what happened and gives them back $3, so each person gets $1 back, making each person's final cost $9.

so 3 x $9 = $27, plus the $2 the bellhop kept is $29. what happened to the other dollar?
 
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Nothing happened to the other dollar. It's conservation of ener... I mean, money :biggrin:.

There's no point in adding 2 dollars.
3 people * $9 = $27 total + $3 returned = $30 initial
$30 initial - ($5 in bellhop hands) = $30 initial - ($3 returned + $2 stolen) = $25 real price

Edit: Solution typo.
 
Last edited:
Psinter said:
Nothing happened to the other dollar. It's conservation of ener... I mean, money :biggrin:.

:smile:...i've actually had people insist that i was lying and each person really got back $1.33.
 
ProfessorLogical said:
:smile:...i've actually had people insist that i was lying and each person really got back $1.33.
Hihi.

You know, I just noticed an error in my equations. Let me edit that... fixed.

Edit: Let me put this in a spoiler so that others who don't want to see the solution can solve it themselves.
I wrote $3 * $9. But the trick is that it is not 3 dollars times 9 dollars. It is 3 people times 9 dollars, which is different. The units are important for it to make sense on the other side of the equation because only if it is expressed as the latter, then can you add the 3 dollars to the 27.

It's fixed now. :smile:
 
It is indeed a sort of play on words, adding things that shouldn't be added. The solution is to "follow the money":
Cashier has $25, bellboy has $2, and the guests have 3x$1 = $30.
 

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