Math Brain Teaser: Where is the $1?

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Discussion Overview

The discussion revolves around a mathematical brain teaser involving a hotel scenario where three guests pay for a room and the distribution of their payment leads to a perceived missing dollar. Participants explore the reasoning behind the apparent discrepancy in the total amounts paid and returned.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant outlines the scenario where three guests pay $30, and after the manager's adjustment, the bellboy keeps $2 and returns $1 to each guest, leading to confusion about the total amount paid.
  • Another participant suggests a conceptual distinction between what is "paid" and what is "held," using the analogy of apples and oranges to clarify the addition of different types of amounts.
  • A later reply emphasizes the trick nature of the problem, explaining that the total amounts can be reconciled by considering the distribution of the money rather than simply adding the amounts together.
  • Some participants propose that the wording of the problem is misleading and that there are multiple ways to approach the solution, indicating a variety of interpretations.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the problem and the reasoning behind the perceived missing dollar. No consensus is reached, as some focus on the trick aspect while others emphasize the mathematical breakdown.

Contextual Notes

Participants note that the problem's wording can lead to confusion, and there are assumptions about how money is categorized and counted that may not be explicitly stated.

Eric DMC
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Three people check into a hotel. They pay $30 to the manager and go to their room. The manager finds out that the room rate is $25 and gives $5 to the bellboy to return. On the way to the room, the bellboy reasons that $5 would be difficult to share among three people, so he pockets $2 and gives $1 to each person. Now, each person paid $10 and got back $1. So they paid $9 each, totalling $27. The bellboy has $2, totalling $29. Where is the remaining dollar?
 
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Eric DMC said:
So they paid $9 each, totalling $27. The bellboy has $2, totalling $29.
Hint:
"Paid" = apples
"has" = oranges
oranges can only be added to oranges
 
DaveC426913 said:
Hint:
"Paid" = apples
"has" = oranges
oranges can only be added to oranges

Count how much money each person started with and how much each person ends up with.
 
Eric DMC said:
Count how much money each person started with and how much each person ends up with.
You know how to read obscured text, right? Select the word "Hint:" - and everything after it...
 
This is actually really simple...

Explanation in white.

This is a trick, really. There are thirty dollars in total. The bellboy takes two, leaving twenty eight dollars. He then gives one to each of the three, leaving twenty five dollars that have been paid. Each person PAYS $9, totaling $27, and then the bellboy takes $2 from that, leaving $25. In total, they paid $25 to the hotel and $2 to the bellboy -- which is $27 total, hence they paid $9 each. The extra three dollars they got in return are invisible, they paid $27 total ($2 to the bell boy, $25 to the rooms,) and now have an extra $1 to pocket.
 
Last edited:
the answer is much simpler than anyone thinks, its just a trick as far as the wording goes. there are two ways to solve this.
1. with math its quite simple. they payed 25 dollars so 25/3 = ($8.333... + 1 [the one they got back]) x 3people = $28 and the bellboy has 2 so that's 30$

2. simple really... the bellboy has 2, the people have 3, and the manager has 25 which in total is 30
 
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