Where Is the Missing Dollar in the Room Rental Puzzle?

  • Context: High School 
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Discussion Overview

The discussion revolves around the "missing dollar" puzzle involving three individuals who rent a room for $30, only to find out the actual cost is $25. The participants explore the reasoning behind the apparent discrepancy in the total amount paid and the money returned, examining it as a brain teaser or a mathematical conundrum.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant presents the puzzle and asks for responses without revealing the solution too early.
  • Another participant questions the calculation of 9*3+2=29, suggesting that the correct breakdown should be 9*3=27, with the remaining $3 summing back to the original $30.
  • Several participants acknowledge familiarity with the puzzle, indicating it is widely known.
  • One participant argues that the problem is more of a tautology than a mathematical issue, providing their own breakdown of the costs and expressing confusion over the perceived dilemma.
  • A different participant notes that the "solution" is clear and suggests that the puzzle is designed to mislead, implying that mathematicians are unlikely to be fooled by it.

Areas of Agreement / Disagreement

Participants express varying levels of familiarity with the puzzle, with some finding it straightforward while others engage in deeper analysis of the reasoning behind the calculations. No consensus is reached on the nature of the puzzle, as some view it as a trick question while others see it as a simple mathematical misunderstanding.

Contextual Notes

Some participants express uncertainty about the formulation of the problem, with one noting difficulty in finding it online, suggesting potential variations in how the puzzle is presented.

mineys
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So there are three guys fresh out of college who want to save money, so they decide to rent a room. The room costs 30 dollars, so they split it 10-10-10. They pay, but it turns out the room is only $25, so the manager asks the bellboy to take $5 and to give it back. The bellboy takes a 'tip' off the top, and gives back $3. So, the paid $9 each. 9*3=27. The bellboy has $2. 9*3+2=$29. Where is the last dollar?

If you know the answer or have heard it before, a simple "oooh, i get it" will suffice. Please do not spoil it for others until they are just about ready to commit suicide.

That is all.
 
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Highlight to read: Why have you done 9*3+2=29? 9*3=27, the total amount paid (25 for the room, 2 to the bellboy), then each person gets one dollar back each, so this sums to 30.[/color]

Note, we have a https://www.physicsforums.com/forumdisplay.php?f=33 forum.
 
Yea I've seen this one before.
 
Ohhh i get it...lol
 
You probably won't catch too many people around here with that one. :D
 
i have heard it before. its a very widely known brain teaser.
 
I think this is more of a tautology and not a maths problem.

The original total cost of the room = $30.00.
Upon review, the total cost of the room is now = $25.00.

This leaves $5.00.

If they bell man takes $2.00, there are $3.00 remaining.

25.00+2.00 = 27 + 3 = 30.

Unless I am an idiot, I don't see the dilemma. I am going to go find the solution to this and see if there is a trick or something -- it seems to straight forward to me (I have never seen this before).

EDIT: can't seem to find this problem when I google it -- did you rewrite it?
 
Last edited:
Well, I'd never heard it before, but the "solution" is clear! Just like any other brain teaser, it's meant to catch you out and disguise the answer. However, as uart says, I don't think many mathematicians will be caught out by it!
 

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