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?

16 comments:

  1. Mr johari,
    our work today was the ancient numerical thing
    do we still do this?

    ReplyDelete
  2. ya when should we hand it up

    ReplyDelete
  3. is the answer 1, 4, 9, 16, 25, 36, 49, 64, 81, & 100?
    i got the answer by calculating the square numbers. total locker is 10 because it is 10square?

    ReplyDelete
  4. i need help for question one a and b i think the ans for a is 99 cause if the locker is visited 4 times it means its is opened closed open and closed again

    ReplyDelete
  5. my answer is
    A 1,4,9,16,25,36,49,64,81 & 100
    B 1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,
    256,289,324,361,400,441,484
    C 60min
    D multiple and guess and check
    E factors and multiples

    ReplyDelete
  6. Group members: Jovan Ng, Ryan Chew, Ian Tay

    c)After an hour.

    d)Factor Tree and Lowest Common Multiple

    e)Yes, factors and multiples.

    ReplyDelete
  7. (c) is 60mins
    (d) LCM--> lowest common multiple
    the ladeer method
    (e) factors and multiples

    ReplyDelete
  8. (C) A, B and C will fall at the same time on the ground every hour.

    (D) Lowest common multiple and guess and check

    (E) Yes there is

    ReplyDelete
  9. group is:

    Brendon Ho
    Denzel Supriyadi
    Sherman Tan
    Shawn Liew

    ReplyDelete
  10. (a) the ans is 76 I used to minus the total numbers of lockers(100)to minus the numbers of prime numbers(25)than you +1

    ReplyDelete
  11. a)
    1
    2
    3
    5
    7
    11
    13
    17
    19
    23
    29
    31
    37
    41
    43
    47
    53
    59
    61
    67
    71
    73
    79
    83
    89
    97
    are open below 100
    Grp members:Nicholas Tan,Kevin,Charles,Matthew

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

    ReplyDelete
  13. b. 1,2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491 and 499 locker are open.

    Group members:Nicholas Tan,Kevin,Charles,Matthew

    ReplyDelete
  14. (b) the ans will be similar and the ans is 405 as the total numbers of prime numbers is 95 so you take 500 - 95 =405
    group members :Choy Rui Zhi
    Malcolm,Yan Kai

    ReplyDelete