Hard problem - dividing the subs

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In summary, the problem is to find the values of n for which the total length of bread, given by the formula n(n+1)/2, can be divided equally among three TAs without breaking any bread. Through finding a pattern and using the formula, it is determined that this is only possible for values of n that are not divisible by 3. To prove this, one can consider the expression \frac{1}{3} \frac{n(n+1)}{2} and how it can only take on values from a specific set due to the restriction on breaking bread.
  • #1
remaan
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Hard problem - dividing the subs !

Homework Statement



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?


Homework Equations


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


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 ?
 
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  • #2


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.
 
  • #3


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 ??
 
  • #4


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:
  • #5


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

What is the "Hard problem - dividing the subs"?

The "Hard problem - dividing the subs" is a theoretical problem in the field of computer science that involves dividing a large dataset or problem into smaller subsets in an efficient and effective manner.

Why is the "Hard problem - dividing the subs" important?

The "Hard problem - dividing the subs" is important because it is a fundamental problem in computer science and has applications in a wide range of fields, such as data analysis, machine learning, and distributed computing. Efficiently dividing a large dataset or problem can greatly impact the performance and accuracy of these applications.

What are some common approaches to solving the "Hard problem - dividing the subs"?

Some common approaches to solving the "Hard problem - dividing the subs" include using algorithms such as partitioning, clustering, and hashing. These algorithms aim to divide the dataset or problem into smaller, more manageable subsets that can be processed separately.

What are the challenges in solving the "Hard problem - dividing the subs"?

One of the main challenges in solving the "Hard problem - dividing the subs" is finding an optimal solution that minimizes the computation time and resources while still maintaining accuracy. Another challenge is handling large and complex datasets, which may require more advanced algorithms and techniques.

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The "Hard problem - dividing the subs" has numerous real-world applications, such as in data mining, image and signal processing, and parallel computing. It can also be used in optimizing resource allocation, load balancing, and data storage in distributed systems.

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