Math Problem Involving 1000 doors

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Discussion Overview

The discussion revolves around a mathematical problem involving 1000 doors, each labeled with a number from 1 to 1000. The problem describes a sequence of actions where a person opens and closes doors based on their factors. Participants are exploring how to determine which doors remain open after all actions are completed, and they are seeking strategies to solve the problem and show their work.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Exploratory

Main Points Raised

  • Some participants describe the initial conditions of the problem, noting that all doors are opened first since every number has 1 as a factor.
  • One participant expresses frustration with their approach of dividing 1000 by successive integers to determine the status of the doors, suggesting it is not an efficient strategy.
  • Another participant begins to analyze specific doors, such as door 1 and door 2, discussing how they are manipulated based on their factors.
  • There is a suggestion to consider the manipulation of doors 3 to 10, indicating a desire to explore the pattern of door status changes further.

Areas of Agreement / Disagreement

The discussion does not show clear consensus, as participants are exploring different methods and expressing uncertainty about the best approach to solve the problem. There are multiple viewpoints on how to analyze the doors and their factors.

Contextual Notes

Participants have not yet established a clear method for solving the problem, and there are unresolved questions about the efficiency of various strategies. The discussion includes repeated statements of the problem, indicating a need for clarification or refinement of the approach.

mck3939
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There are 1000 doors. Each one labeled with a number 1-1000. A person opens all doors whose number has one as a factor (which is all of them). Then she closes all doors whose number has two as a factor. Then the person continues to change the status of the doors (opening or closing them) based on the number and factors. What lockers will be open when we reach 1000? How do you show your work?
 
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Hi. Welcome to MHB. (Wave) We ask you to post any work you have tried or any effort and to explain where you are stuck or having trouble therefor our math helpers or anyone who can help has a better idea and understanding of what you have tried so far and where you are standing/stuck. Thank You. :)
 
There are 1000 doors. Each one labeled with a number 1-1000. A person opens all doors whose number has one as a factor (which is all of them). Then she closes all doors whose number has two as a factor. Then the person continues to change the status of the doors (opening or closing them) based on the number and factors. What lockers will be open when we reach 1000? How do you show your work?

I tried first dividing 1000 by 2 to get 500
then 1000 by 3 to get approximately 333
and 1000 by 4 and so on, but I find this is taking forever and is no the best strategy to use. I cannot think of a better one.
 
mck3939 said:
There are 1000 doors. Each one labeled with a number 1-1000. A person opens all doors whose number has one as a factor (which is all of them). Then she closes all doors whose number has two as a factor. Then the person continues to change the status of the doors (opening or closing them) based on the number and factors. What lockers will be open when we reach 1000? How do you show your work?

I tried first dividing 1000 by 2 to get 500
then 1000 by 3 to get approximately 333
and 1000 by 4 and so on, but I find this is taking forever and is no the best strategy to use. I cannot think of a better one.

Hi mck3939! Welcome to MHB! :)

Let's start with door 1.
We open it... and we're done, since 1 is the only number that divides 1.

Next is door 2, which is a prime.
We open it, we close it, and we're done.
So we manipulate it twice, since 1 and 2 are the only numbers that divide 2.

How about, say, doors 3 to 10? (Wondering)
 

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