Where's the Change? 3 Men Share a Hotel Room

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Discussion Overview

The discussion revolves around a classic mathematical riddle involving three men sharing a hotel room and the confusion surrounding the distribution of money after a special rate is applied. Participants explore the implications of the riddle, its misleading nature, and various interpretations of the financial transactions involved.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants note that the riddle is misleading, suggesting that the way the problem is framed causes confusion about the total amount paid and the tip.
  • One participant proposes that the men actually paid $9 each, totaling $27, which includes the $25 for the room and a $2 tip, questioning the logic behind adding the tip again.
  • Another participant suggests that the problem is designed to trick the reader by counting the tip twice.
  • A different viewpoint mentions using a debit/credit approach to clarify that there is no extra dollar, as the total disbursed matches the expenses incurred.
  • Some participants express frustration with the riddle, describing it as "evil" and noting the difficulty in explaining it to others.
  • One participant humorously suggests that the missing dollar could be "on wolfram's bed," indicating a playful take on the confusion.

Areas of Agreement / Disagreement

Participants generally agree that the riddle is misleading and that the confusion arises from the way the financial transactions are presented. However, there are multiple interpretations of how to understand the distribution of the money, and no consensus is reached on a definitive explanation.

Contextual Notes

Some participants highlight the importance of understanding how the tip is accounted for in the total payment, indicating that assumptions about the distribution of money may vary among individuals.

Who May Find This Useful

This discussion may be of interest to those exploring mathematical puzzles, logic problems, or the psychology of reasoning and misdirection in problem-solving.

RunDMC
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Three men go to a hotel and decide to share a room. The room costs $30 per night, so they each leave $10 at reception and head upstairs.

Later the concierge recalls that tonight is the twenty-five-dollar special. He gives the bell hop exactly five one-dollar coins(/notes, depends on your currency!).

The bell hop arrives at the room and explains the special. The men realize there is no easy way to share the 5 coins between them, so they keep one dollar each and give the bell hop a $2 tip.

Later, one of the men exclaims: "Wait, we got $1 back each, right? Well, that means we paid $9 each for the room, right? (Our original $10 each minus the dollar we got back.) Now, three nines is 27, plus the $2 tip gives $29. Where'd the other dollar go?"

Where, indeed, did the extra dollar go?
 
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Oh this is so old :P
 
Pengwuino said:
Oh this is so old :P
I concur.
.
 
Its fairly obvious that the 2nd man ate the money
 
Government tax.
 
try thinking of it this way: 3 guys go to rent a room. it costs 25 a night. to make it even they each pay 9 dollars and say keep the change. 3*9=27total=25rent+2tip. they didn't pay 27+2.
 
Must be a sign of the times, these 3 guys used to just go out for a meal, now they're sharing a room for the night!
 
It's easy! the question is set up to mislead you... it's really like this... 30$ is payed... 5$ is given back (now we're at 25$ payed) ... 3 dollars are kept (now we're at 28!) 2 dollar tip! wala... 30$... each man does not actually pay the even 9 dollars each :P... but where indeed... does that extra penny go? It's only 25 dollars for the room! Why would they each pay 9 dollars? :P 8.33X3 is 24.99, kept 3, 27.99, 2 tip... 29.99... where is the extra penny? haha i suck at my futile attempts to keep this going.
 
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I am just a normal housewife...no big education...but I would use the debit/credit theory...
debit...$27 disbursed collectively from the 3 men

credit...$25 for the room and $2 tip...

No extra dollar floating around:rolleyes:
 
  • #10
It's on wolfram's bed :smile:
 
  • #11
It's such an evil problem. They count the tip twice, it was already included in the 27$ and for some reason they add it again.
 
  • #12
Alkatran said:
It's such an evil problem. They count the tip twice, it was already included in the 27$ and for some reason they add it again.

Werd.
It's an easy problem :)

However, I should try to get some people with that type of logic...hmm
 
  • #13
I was a bit perplexed a first, I was wondering why he added the two dollars to 27 when he should have been subtracting it to get the cost of the room. Funny, misleading the person like so; I wonder how many of my friends will fall for it?
 
  • #14
So how do I explain this to everybody so I sound smart?
 

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