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?

13 comments:

  1. Question about the droplets...
    c)60mins
    d)ladder division & listing of fsctors
    e)Lowest common multiple(LCM)

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  2. Names: Isaac, Hamidshah, Darren
    (c): 60
    (d): Prime Factorisation and making a Time Line
    (e): Lowest Common Multiples

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  3. questions of the lockers :
    Ans :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.
    We used the Sieve Of Eratosthenes.
    Jean Yee, Jamie and Dylaine

    ReplyDelete
  4. For part A locker problem: lockers,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
    For part B:All the prime numbers from 1 to 500

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  5. This comment has been removed by the author.

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  7. Task 2:
    c) 60 mins
    d) Ladder division and lowest common multiple.
    e) Lowest Common Multiple (LCM)

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  8. a) Ans :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.
    We used the Sieve Of Eratosthenes.

    b) 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
    467 479 487 491 499

    c) 60min
    d)LCM and long division
    e)Lowest Common Multiple

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  9. Task 1
    Name:Nicholas,Dominic,Cameron
    a)Ans: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
    Method:Sieve of Eratosthenes
    b)Ans: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
    467 479 487 491 499
    Task 2
    c)60minutes later
    d)Factor tree,repeated division/ladder division
    e)Lowest Common Multiple(LCM)

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  10. Names:Saishwar & Princeton
    a)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
    b)2, 3, 5, 7, 11, 13 ,17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 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, 11, 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, 01, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499.
    c) Every 1h
    d)Factor Tree and long division
    e)Factors and Multiples (LCM)

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  11. Task 1:
    a) 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. We found the square numbers till 100.

    b) 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121,144, 169, 196, 225, 256, 289, 324, 361, 441, 484. We found the square numbers till 500.

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  13. Name: Nathaniel Yeo, Yong Ming Yang
    (a)1,4,9.. and all the other square numbers to 100.
    (b)Square number from 1 to 500
    Droplets answer: (a) 60mins later(find the LCM of the numbers.)
    (b)Factor tree and the ladder division method.
    (c)LCM (Lowest Common Multiple)

    ReplyDelete