Thursday, January 13, 2011

Problem Solving: the Locker Problem

An impending headache to the administrator in planning the locker operation in SST. He seeks your advise on how to resolve this issue:

Here is the problem:
In SST, there is a row of 100 closed lockers numbered 1 to 100. A student goes through the row and opens every locker. A second student goes through the row and for every second locker if it is closed, she opens it and if it is opened, she closes it. A third student does the same thing for every third, a fourth for every fourth locker and so on, all the way to the 100th locker. 
source:  seas.gwu.edu
The goal of the problem is to determine which lockers will be open at the end of the process.

TASK 1
Working in pairs, explain your thinking to the following problems clearly. Be sure to use appropriate mathematical language and methods. Post your answers in the comment and indicate both of your names.
(a) Which lockers remain open after the 100th student has passed?
(b) If there were 500 students and lockers, which lockers remain opened after the 500th student has passed?

TASK 2 (similar problem)
3 droplets of water fell at the following rate, droplet A at every 5 minutes interval, droplets B at every 12 minutes interval and droplets C at every half an hour interval. 
source: unreasonablydangerousonionrings.blogspot.co
(c) When do you think all the droplets, that is A, B and C will fall at the same time on the ground? 
(d) Identify at least 2 methods to solve this problem. 
(e) Is there a particular topic in maths that analyses such problems?

21 comments:

  1. 1a) 10 lockers remain open.
    1b) 22 lockers remain open.

    2a) 60 minutes after they first drop together.
    2bi) Lowest common multiple.
    In this case, the numbers used are 5, 12, and 30. The lowest common multiple of these numbers is 60.
    2bii) The table method.
    This method, as its name says, uses a table.

    ReplyDelete
  2. Task 1a lockers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
    Task 1b lockers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484
    Task 2a They will fall at same time at the 60th minute/1st hour
    Task 2b Method 1: Find the common multiple of 5, 12 and 30.
    Method 2: Make a graph and list out all the times that each droplet drops.
    Task 2c Patterns

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  3. 1a) 10 lockers remain open
    1b) 22 lockers remain open
    2a) 1 hour after their first drop
    2b) Lowest Common Multiple
    Algebra/ Guess and Check
    2c) HCF and LCM: Highest Common Factors and Lowest Common Multiples

    Members: Carissa, Valery, Chelsea, Wei Qin

    ReplyDelete
  4. Task 1A locker:1,4,9,16,25,36,49,64,81,100
    Task 1B locker:1,4,9,16,25,36,49,64,81,100,121,144,169,225,256,289,324,361,400,441,484
    Find the square roots of the numbers which is under 100 for a and 500 for
    Task 2a:They will fall at same time at the 60th minute/1st hour
    Task 2b:Lowest common multiple
    Method: algebra/guess and check
    Task 2c:highest common factors and lowest common multiples

    ReplyDelete
  5. This comment has been removed by the author.

    ReplyDelete
  6. Task 1A locker:1,4,9,16,25,36,49,64,81,100
    Task 1B locker:1,4,9,16,25,36,49,64,81,100,121,144,169,225,256,289,324,361,400,441,484
    Method:Find the square roots of the numbers which is under 100 for A and 500 for B.
    Task 1c: After 1 hour.
    Task 1d.Lowest Common Multiple and Guess and Check
    Task 1e. Patterns
    Done with Darshan

    ReplyDelete
  7. 1a)10 lockers:1,4,9,16,25,36,49,64,81,100
    1b)22 lockers: 1,4,9,16,25,36,49,64,81,100,121,144,169,225,256,289,324,361,400,441,484
    2a)1 hour after their first drop
    2b)Lowest Common Multiple
    Method:Guess and Check
    2c):Highest Common Factors and Lowest Common Multiple

    ReplyDelete
  8. Task 1a) 1,4,9,16,25,36,49,64,81.100
    Task 1b) 1,4,9,16,25,36,49,64,81.100, 121, 144, 169, 196,225,256,289, 324, 361, 400,441, 484

    Task 2a) 1 hour/60 min
    Task 2b) Lowest Common Multiple/Listing
    Task 2c) Data Anylasis

    Group Members: Bowen, Ryan Lai, Sherwin

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  9. Task 2 a) 60 min
    b) find common multiples and use guess and check
    c) factors and multiples

    ReplyDelete
  10. i'm stuck at task 1 anyone help me

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  11. Task 1a) 10 lockers: 1,4,9,16,25,36,49,64,81,100
    Task 1b) 22 lockers: 1,4,9,16,25,36,49,64,81.100,121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484

    Task 2a) 60 minutes
    Task 2b) Find the smallest common multiple of 5, 12 and 30
    Task 2c) List out the time past as the waters drip, making a list

    ReplyDelete
  12. Task 1A is locker:1,4,9,16,25,36,49,64,81,100
    Task 1B is locker:1,4,9,16,25,36,49,64,81,100,121,144,169,225,256,289,324,361,400,441,484
    Method:Find the square roots of the numbers which is under 100 for A and 500 for B.
    Task 1c: After 1 hour time
    Task 1d.Lowest Common Multiple, Guess and Check
    Task 1e. Patterns Done with Wai Kit

    ReplyDelete
  13. This comment has been removed by the author.

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  14. Task 1a) 1,4,9,16,25,36,49,64,81,100 (10 lockers)
    Task 1b) 1,4,9,16,25,49,64,81,100,121,144,169,196,225,256,289,324,361,400,441,484 (22 lockers)

    Task 2a) 60 minutes
    Task 2b) Find the smallest common multiple of 5,12 and 30/ Guess and Check
    Task 2c) Patterns

    ReplyDelete
  15. 1a) lockers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
    1b) lockers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484

    2a) 60min
    2b i) Find the smallest common multiple of 5,12 and 30(60)
    2b ii) Make a table
    2c)Multiples and factors

    ReplyDelete
  16. This comment has been removed by the author.

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  17. Task 1a 10 lockers: 1,4,9,16,25,36,49,64,81,100
    Task 1b not sure


    Task 2a 60 minutes
    Task 2b LCM and Guess and check
    Task 1e Factors and Multiples

    ReplyDelete
  18. Task 1: A)10 lockers that are>1,4,9,16,25,36,49,64,81,100(square numbers)
    B)all square numbers from 1 to 500>1,4,9,16,25,36,49,64,81,100,121,144...
    Task 2:C)60 minutes
    D) FIRST METHOD: find the lowest common multiple of all the numbers using 30mins as the reference.
    SECOND METHOD: unsure
    E) this years first unit: factors and multiples

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  19. Task 1a 10 lockers: 1,4,9,16,25,36,49,64,81,100
    Task 1B Lockers :1,4,9,16,25,36,49,64,81,100,121,144,169,225,256,289,324,361,400,441,484

    Task 2c: 60 Minutes
    Task 2d: Listing of multiples and lcm
    Task 2e : Multiples


    Done With Lindsay

    ReplyDelete