Where Did the Last Dollar Go in the Hotel Room Puzzle?

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    Mystery
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Discussion Overview

The discussion revolves around a classic puzzle involving a hotel room charge and the distribution of money among three men and a bellboy. Participants explore the apparent paradox of missing money when the total payments and refunds are calculated. The scope includes conceptual reasoning and mathematical interpretation of the scenario.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant asserts that the calculation leading to the missing dollar is incorrect, stating that the claim of making 29 dollars is wrong.
  • Another participant clarifies that the total amount paid by the men is 27 dollars, which consists of 25 dollars for the hotel and 2 dollars kept by the bellboy.
  • A different participant suggests that the confusion arises from incorrectly adding amounts that should not be combined, likening it to a flawed reasoning process.
  • One participant reiterates the original puzzle statement, emphasizing the confusion around the total amounts paid and kept, and suggests that no money is unaccounted for.
  • Another participant describes the situation as an exercise in semantics, indicating a focus on the language and reasoning used in the puzzle.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the puzzle and the calculations involved. There is no consensus on a definitive resolution to the apparent paradox, with multiple competing explanations presented.

Contextual Notes

The discussion highlights limitations in reasoning and the potential for misunderstanding in the way the amounts are framed and calculated. The participants do not resolve the mathematical steps or assumptions underlying their arguments.

CaptainQuaser
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Three guys walk into a hotel. The Bell boy charges them 30 dollars for the room. Each of the thee men pay 10 dollars.

The Bell boy gives the money to the manager but is repremanded as the room only costs 25 dollars, he is told to give 5 dollars back.

To make things easier he gives each man 1 dollar back and keeps 2 for himself.

So in the end each man had paid 9 dollars making 27 in total. The Bell boy kept 2 making 29, so where did the last dollar go?
 
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nowhere. 2making 29 is wrong.
 
captain, welcome to PF!
thanks for contributing to the puzzles
having new people bring puzzles (even if sometimes there might be repeats) keeps things lively

I'll hide an answer to show how it is done if you are not familiar with it.
You put the answer between [C*LOR=white] and [/C*LOR]
but spell it color, not c*lor
so run the mouse over the next patch of area and it will show up

the guys paid out a total of 27 dollars, where did the 27 dollars go? the bellhop got $2 and the manager got $25
I think this is what neurocomp is saying
 
yes...sorry i guess i should have whited out my answer. my bad.
 
CaptainQuaser said:
Three guys walk into a hotel. The Bell boy charges them 30 dollars for the room. Each of the thee men pay 10 dollars.

The Bell boy gives the money to the manager but is repremanded as the room only costs 25 dollars, he is told to give 5 dollars back.

To make things easier he gives each man 1 dollar back and keeps 2 for himself.

So in the end each man had paid 9 dollars making 27 in total. The Bell boy kept 2 making 29, so where did the last dollar go?

:confused: The men only pay 25 dollars, because the manager gives 5 dollars back. so when the bell boy gives them each 1 dollar, that makes it 28 dollars and the boy keeps 2 dollars which makes it 30 dollars. Therefore the men pay uneven amounst of money, but no money is unaccounted for. :confused:
 
CaptainQuaser said:
Three guys walk into a hotel. The Bell boy charges them 30 dollars for the room. Each of the thee men pay 10 dollars.

The Bell boy gives the money to the manager but is repremanded as the room only costs 25 dollars, he is told to give 5 dollars back.

To make things easier he gives each man 1 dollar back and keeps 2 for himself.

So in the end each man had paid 9 dollars making 27 in total. The Bell boy kept 2 making 29, so where did the last dollar go?
exercise in symamtics
 
"So in the end each man had paid 9 dollars making 27 in total. The Bell boy kept 2 making 29, so where did the last dollar go?"

Answer:
This last statement is adding apples and oranges; it is trying to add "amount given out" to "amount received" and then asking why they don't add up.
It's like saying "I pay you $5, and you receive $5. If we add those together, we have suddenly created a total of $10 out of nothing."

In reality, the sum total of moneys started off at $30 (all in the men's hands) In the end, the hotel has $25, the bellboy has $2 and the 3 men have $1 each.
 

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