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Hard problem - dividing the subs

  1. Sep 5, 2010 #1
    Hard problem - dividing the subs !!

    1. The problem statement, all variables and given/known data

    Anupam brought n > 0 subs, one each of length 1; 2; 3;....... ; n, to a grading party.
    The three TAs distributed the subs among themselves such that no sub was broken, and each TA
    ended up with an equal total length. For what values of n is such a division possible?


    2. Relevant equations
    At some point, we may use the the sum formula : n(n+1)/2


    3. The attempt at a solution

    I tried finding a pattern

    n = 1
    we have only one sub, doesn't work

    n= 2
    doesn't work

    n=3
    doesn't work, as we can't divide this by 3 people.

    n=4
    doesn't work,

    n= 5
    it works !!
    we have 1,2,3,4,5
    we can divide by 3 as follows :
    one of the TAs will take 5
    The other will take 4,1
    The third will take 2,3

    So, how should I precede with that ?

    Do you think this is the right thing ?
     
  2. jcsd
  3. Sep 5, 2010 #2
    Re: Hard problem - dividing the subs !!

    It's good that you looked for a pattern right off the start, but I think the main focus is in the formula they gave you (n(n+1)/2). This formula is the what you would use to find 1 + 2 + 3 +...+n. So in the context of this question (n(n + 1))/2 gives you the total length of bread that will be available.
    Hope this helps.
     
  4. Sep 6, 2010 #3
    Re: Hard problem - dividing the subs !!

    Mmm...
    Ya But the problem with that is:
    Knowing how long bread I have Doesn't solve the problem, since
    I Am not Able to break the breads apart.

    So, any extra hints ??
     
  5. Sep 6, 2010 #4
    Re: Hard problem - dividing the subs !!

    Think about each bread as an integer. The fact that we can't break apart any bread when we divide the total length by 3 is important as it tells us something about the expression:
    [tex]\frac{1}{3}[/tex] [tex]\frac{n(n+1)}{2}[/tex] , mainly that it can only take on values from a specific set.
    Hope this helps
     
    Last edited: Sep 6, 2010
  6. Sep 6, 2010 #5
    Re: Hard problem - dividing the subs !!

    Ok. now suppose I found the two numbers -
    are there any hints of how to prove them ?
     
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