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[HELP!] Math/scheduling puzzle that has me stumped

Discussion in 'BBS Hangout' started by BetterThanI, Aug 18, 2011.

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  1. BetterThanI

    BetterThanI Contributing Member

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    Okay, this isn't just an intellectual exercise, it's a real-world problem. I've been trying solve it, but just can't figure it out.

    Here it is: there are five days in the week: M T W Th F

    There are five teachers: A, B, C, D, E

    There are three rotation stations: 1. Art, 2. Music, 3. Gym

    Parameters:

    - They need three days a week with gym, one with art, and one with music.

    - Gym can teach one, two, or three classes at a time, but no more than three.

    - Trying to make it so that they never have gym two days in a row.


    Options

    - 1 or 2 classes could be divided into 1/2, 1/4, even 1/5.

    - A two week rotation (A/B week) is an option, though not a necessity.


    Rep points awarded to whomever can solve this.
     
    #1 BetterThanI, Aug 18, 2011
  2. ToyCen428

    ToyCen428 Member

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    Weird clouds are weird. :)
     
    #2 ToyCen428, Aug 18, 2011
  3. Xerobull

    Xerobull You son of a b!tch! I'm in!

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    Simple answer:

    All of them, my pad, baby!

    [​IMG]
     
    #3 Xerobull, Aug 18, 2011
  4. candlegreen

    candlegreen Contributing Member

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    This is all assuming that this all happens at the same time per day?

    I don't see how you could push it so there are no gym days going 2 in a row.

    If they need 3 gym days a week and there are 5 days, they have to be M/W/F regardless of 1 or 2 week rotation schedules.

    If you can't fit all 5 classes on those days, it really doesn't matter how you do it if they need 3 a week.

    Also, splitting into 1/2s, 1/4s, etc. does not help in this situation at all.
     
    #4 candlegreen, Aug 18, 2011
    Last edited: Aug 18, 2011
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  5. Qball

    Qball Contributing Member

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    Each class can go to only 1 rotation (gym, art, or music) per day? Basically wondering if Class A can go to gym and art on Monday...
     
    #5 Qball, Aug 18, 2011
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  6. candlegreen

    candlegreen Contributing Member

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    Do they have to share the same time slot?

    3 classes at the same time at the gym. Are there other time slots? If so, then it's easy.
     
    #6 candlegreen, Aug 18, 2011
  7. B-ball freak

    B-ball freak Contributing Member

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    Unless all of them go to gym M, W, F, then there is no way that at least one class won't have it two days in a row.

    Have 1 go M,W,Th - 1 go T,W,F - 1 go M,T,Th - 1 go T,Th,F- and 1 M,W,F

    That has 3 classes per day with each class sharing gym at least once with the other 4.
     
    #7 B-ball freak, Aug 18, 2011
    Last edited: Aug 18, 2011
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  8. BetterThanI

    BetterThanI Contributing Member

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    Some points to clarify:

    - Yes, the classes all happen simultaneously (i.e. - one class in art, one class in music, up to three classes in the gym, all at 8:00am-9:00am).

    - No, going to gym and music/art in one rotation (i.e. - 8:00-8:30 gym, 8:30-9:00 music) is NOT an option.
     
    #8 BetterThanI, Aug 18, 2011
  9. SwoLy-D

    SwoLy-D Contributing Member

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    Although his seems like something the computers at IBM would schedule out in the Olympics, I can't visualize what you want. :(

    Please show me an example and why it DOESN'T work... like, for example, one teacher's entire week and how it looks, and how you would do this for a different teacher that meets the required parameters you explained.

    He also mentioned that it could be that there are two weeks, rotated. I'll use "R" for Thursday like we do in the university system:

    Teacher A
    ---------
    Week 1:
    M gym
    W gym
    F gym
    Week 2:
    T gym
    R gym

    ^ 2-week rotation, gym without 2 days in a row, but I don't have the times. Is that good, BetterThanI? :confused:
     
    #9 SwoLy-D, Aug 18, 2011
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  10. rolyat93

    rolyat93 Contributing Member

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    Gym, Tan, Laundry.
     
    #10 rolyat93, Aug 18, 2011
  11. BetterThanI

    BetterThanI Contributing Member

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    Not bad, but they would need another day in the gym in Week 2 (i.e. - T Th R)> Let's see if this helps visualize. Here is the current schedule:

    [​IMG]

    The problem with the schedule as it currently sits is that PE needs to teach three lessons per week, and they need to be in order (1,2,3 - in ed, we call it sequenced teaching). So, on Monday, classes B, D, and E receive Lesson 1. What do they do on Tuesday? They can't really teach Lesson 2, because classes C and A come on Tuesday, and the didn't get Lesson 1 yet. They can't teach Lesson 1, because class D already had it and needs to move on to the next lesson or they'll be one hour behind.

    Help me, Obi Wan Kenobi! You're my only hope!
     
    #11 BetterThanI, Aug 18, 2011
  12. Ender120

    Ender120 Contributing Member

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    <embed id=VideoPlayback src=http://video.google.com/googleplayer.swf?docid=-6456673973219229574&hl=en&fs=true style=width:400px;height:326px allowFullScreen=true allowScriptAccess=always type=application/x-shockwave-flash> </embed>
     
    #12 Ender120, Aug 18, 2011
  13. fadeaway

    fadeaway Contributing Member

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    Use linear programming in Excel Solver to figure this out.
     
    #13 fadeaway, Aug 18, 2011
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  14. candlegreen

    candlegreen Contributing Member

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    that won't fit the 3 gyms a week on week 2 though.
     
    #14 candlegreen, Aug 18, 2011
  15. candlegreen

    candlegreen Contributing Member

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    The problem is that you don't want 2 PE days in a row. If this situation you've listed is your issue, then must you teach in order? I assume that's the case since it's "sequence teaching." I assume you can't teach lesson 2 before lesson 1 for a specific class?
     
    #15 candlegreen, Aug 18, 2011
  16. BetterThanI

    BetterThanI Contributing Member

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    Nope, can't do it. Need to go in order: 1,2,3.
     
    #16 BetterThanI, Aug 18, 2011
  17. JayZ750

    JayZ750 Contributing Member

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    With the sequential teaching requirement added, I don't see how it's possible, even if they go to PE on back to back days.
     
    #17 JayZ750, Aug 18, 2011
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  18. rage

    rage Member

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    Who are they?
    What is gym? Gym class, gym teacher?
    Who are they?

    What does this mean?

    Can any of the teachers A-D teach any class?
     
    #18 rage, Aug 18, 2011
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  19. BetterThanI

    BetterThanI Contributing Member

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    Yeah, I got a little vague with my indefinite pronouns. Sorry. Let me clarify: The students are required to spend three days a week in gym class, one day in art class, and one day in music class.


    The gym teachers can teach one, two, or three classes at a time, but no more than three.

    Correction: trying to make it so that the students never have gym two days in a row.

    No, the teachers A-E aren't teaching gym, art, or music. A-E are the homeroom teachers. Gym, art, and music have dedicated teachers that teach the students from classes A-E.

    I'm convinced now that it is impossible to fulfil my set parameters, given the number of classes and days in which to schedule. Makes me feel a bit better, since I struggled with this for almost 3 hours and still couldn't make it work. Thanks for trying though, guys. Rep for everyone!
     
    #19 BetterThanI, Aug 18, 2011
  20. heypartner

    heypartner Contributing Member

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    haven't read other responses but this should be simple. however, this parameter needs more explanation

    - Gym can teach one, two, or three classes at a time, but no more than three.

    you introduce the notion of "classes" as a rule in your parameters, but you don't define what a "class" means vs a day.
     
    #20 heypartner, Aug 18, 2011
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