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

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Discussion Overview

The discussion revolves around a classic mathematical puzzle known as "The Mystery of the Missing Dollar," which involves a scenario with three individuals paying for a hotel room and the subsequent confusion regarding the distribution of money. The focus is on the reasoning behind the perceived missing dollar and the implications of the transactions involved.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant describes the scenario of three people paying for a hotel room and the subsequent return of money by the bellhop, leading to confusion about the total amount paid.
  • Another participant asserts that nothing happened to the missing dollar, suggesting a misunderstanding of the conservation of money.
  • A participant mentions that they have encountered others who mistakenly believe that each person received back $1.33 instead of $1.
  • One participant acknowledges an error in their earlier calculations and indicates a desire to clarify the solution without revealing it to others who may wish to solve the puzzle independently.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the puzzle, with some asserting that there is no missing dollar while others seem to misunderstand the distribution of the money. The discussion remains unresolved with multiple competing interpretations present.

Contextual Notes

Participants reference errors in calculations and misunderstandings about the distribution of money, indicating that assumptions about the problem may not be universally shared.

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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