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October 28th, 2010, 01:21 PM   #1
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very hard question

could someone help with this please,

Let k be a non-negative integer. How many distinct integer-valued vectors (n1, n2, . . . , nr) are there which satisfy both of the following constraints?

nj ?k for all j=1,2,...,r
and
n1 + n2 + + nr = n.
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November 2nd, 2010, 01:52 PM   #2
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Re: very hard question

I think its
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November 2nd, 2010, 02:20 PM   #3
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Re: very hard question

Yes, that's right. Clearly only makes sense for
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November 3rd, 2010, 04:59 PM   #4
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Re: very hard question

how do you get to that solution. i dont uinderstnad the working leading up to it :S
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November 3rd, 2010, 06:22 PM   #5
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Re: very hard question

Consider it this way.

You have n balls, you have to put them in r bins. Each bin must have k balls, that leaves n - rk balls to distribute. There are r bins to put them in.

This is now a simplified partition problem.
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