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	<title>Comments on: Free RapidShare Account by Solving a Math Problem</title>
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	<link>http://www.liewcf.com/blog/archives/2006/10/free-rapidshare-account-by-solving-a-math-problem/</link>
	<description>Tech, Web, How to, Reviews, Tips, Downloads, and Make Money Online</description>
	<pubDate>Thu, 20 Nov 2008 16:21:28 +0000</pubDate>
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		<item>
		<title>By: Kunal</title>
		<link>http://www.liewcf.com/blog/archives/2006/10/free-rapidshare-account-by-solving-a-math-problem/#comment-270009</link>
		<dc:creator>Kunal</dc:creator>
		<pubDate>Wed, 28 Feb 2007 16:32:27 +0000</pubDate>
		<guid isPermaLink="false">http://www.liewcf.com/blog/?p=2647#comment-270009</guid>
		<description>want rapidshare, megaupload, megashare, filefactory, depositefiles account ??
no one can give it to you except me if anyone of you make 300 posts on my forum !! - www.dhoom.bigbig.com , here you can find everything to download if you register and give links which you know !!</description>
		<content:encoded><![CDATA[<p>want rapidshare, megaupload, megashare, filefactory, depositefiles account ??<br />
no one can give it to you except me if anyone of you make 300 posts on my forum !! - <a href="http://www.dhoom.bigbig.com" rel="nofollow">http://www.dhoom.bigbig.com</a> , here you can find everything to download if you register and give links which you know !!</p>
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	</item>
	<item>
		<title>By: darks</title>
		<link>http://www.liewcf.com/blog/archives/2006/10/free-rapidshare-account-by-solving-a-math-problem/#comment-265636</link>
		<dc:creator>darks</dc:creator>
		<pubDate>Thu, 22 Feb 2007 11:50:54 +0000</pubDate>
		<guid isPermaLink="false">http://www.liewcf.com/blog/?p=2647#comment-265636</guid>
		<description>there are not working 

please give me working premium accounts</description>
		<content:encoded><![CDATA[<p>there are not working </p>
<p>please give me working premium accounts</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: Cristi</title>
		<link>http://www.liewcf.com/blog/archives/2006/10/free-rapidshare-account-by-solving-a-math-problem/#comment-264288</link>
		<dc:creator>Cristi</dc:creator>
		<pubDate>Tue, 20 Feb 2007 12:06:27 +0000</pubDate>
		<guid isPermaLink="false">http://www.liewcf.com/blog/?p=2647#comment-264288</guid>
		<description>10^n-10^(n-1)</description>
		<content:encoded><![CDATA[<p>10^n-10^(n-1)</p>
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	<item>
		<title>By: sd</title>
		<link>http://www.liewcf.com/blog/archives/2006/10/free-rapidshare-account-by-solving-a-math-problem/#comment-261704</link>
		<dc:creator>sd</dc:creator>
		<pubDate>Sat, 17 Feb 2007 10:41:19 +0000</pubDate>
		<guid isPermaLink="false">http://www.liewcf.com/blog/?p=2647#comment-261704</guid>
		<description>latest archive of hacked rapidshare accounts just for anyone who wants piracy : 
by : 

 //mtl\\__hacking__//mtl\\ Group 

it just works untill 28 mar 2007

http://rapidshare.com/files/16841447/Rapidshare_Premium_-_feb-mar_2007.rar

enjoy that my friend :)</description>
		<content:encoded><![CDATA[<p>latest archive of hacked rapidshare accounts just for anyone who wants piracy :<br />
by : </p>
<p> //mtl\\__hacking__//mtl\\ Group </p>
<p>it just works untill 28 mar 2007</p>
<p><a href="http://rapidshare.com/files/16841447/Rapidshare_Premium_-_feb-mar_2007.rar" rel="nofollow">http://rapidshare.com/files/16841447/Rapidshare_Premium_-_feb-mar_2007.rar</a></p>
<p>enjoy that my friend <img src='http://www.liewcf.com/blog/wp-includes/images/smilies/icon_smile.gif' alt=':)' class='wp-smiley' /></p>
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		<title>By: johnny</title>
		<link>http://www.liewcf.com/blog/archives/2006/10/free-rapidshare-account-by-solving-a-math-problem/#comment-261327</link>
		<dc:creator>johnny</dc:creator>
		<pubDate>Fri, 16 Feb 2007 22:15:17 +0000</pubDate>
		<guid isPermaLink="false">http://www.liewcf.com/blog/?p=2647#comment-261327</guid>
		<description>Here's the latest RS accounts guys, tested and checked as of 21:48 16.02.2007
Please dont change passwords!

http://rapidshare.com/files/16802515/RS_Accounts_Feb_2007.rar</description>
		<content:encoded><![CDATA[<p>Here&#8217;s the latest RS accounts guys, tested and checked as of 21:48 16.02.2007<br />
Please dont change passwords!</p>
<p><a href="http://rapidshare.com/files/16802515/RS_Accounts_Feb_2007.rar" rel="nofollow">http://rapidshare.com/files/16802515/RS_Accounts_Feb_2007.rar</a></p>
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	<item>
		<title>By: Iceman</title>
		<link>http://www.liewcf.com/blog/archives/2006/10/free-rapidshare-account-by-solving-a-math-problem/#comment-259417</link>
		<dc:creator>Iceman</dc:creator>
		<pubDate>Wed, 14 Feb 2007 06:57:13 +0000</pubDate>
		<guid isPermaLink="false">http://www.liewcf.com/blog/?p=2647#comment-259417</guid>
		<description>clearly we have x1+x2+......xN = s
and all x are integers between 0 and 9 and also x1 cannot be zero.

now represent as powers
 
A^(x1+x2......) = A^s
using the fact that we all x can take one of fixed values 
=&#62; left side is:
(1+A+A^2......A^9)^(N-1)*(A+A^2........A^9)   (because x1 cannot take zero).

therefore take coefficient of A^s in this expansion to get answer.
= coeff of A^s in (1+A+A^2......A^9)^(N-1)*(A+A^2........A^9)

This will work even for s</description>
		<content:encoded><![CDATA[<p>clearly we have x1+x2+&#8230;&#8230;xN = s<br />
and all x are integers between 0 and 9 and also x1 cannot be zero.</p>
<p>now represent as powers</p>
<p>A^(x1+x2&#8230;&#8230;) = A^s<br />
using the fact that we all x can take one of fixed values<br />
=&gt; left side is:<br />
(1+A+A^2&#8230;&#8230;A^9)^(N-1)*(A+A^2&#8230;&#8230;..A^9)   (because x1 cannot take zero).</p>
<p>therefore take coefficient of A^s in this expansion to get answer.<br />
= coeff of A^s in (1+A+A^2&#8230;&#8230;A^9)^(N-1)*(A+A^2&#8230;&#8230;..A^9)</p>
<p>This will work even for s</p>
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	<item>
		<title>By: chris davis</title>
		<link>http://www.liewcf.com/blog/archives/2006/10/free-rapidshare-account-by-solving-a-math-problem/#comment-257314</link>
		<dc:creator>chris davis</dc:creator>
		<pubDate>Sun, 11 Feb 2007 05:56:43 +0000</pubDate>
		<guid isPermaLink="false">http://www.liewcf.com/blog/?p=2647#comment-257314</guid>
		<description>The sum of proper divisors gives various other kinds of numbers. Numbers where the sum is less than the number itself are called deficient, and where it is greater than the number, abundant. These terms, together with perfect itself, come from Greek numerology. A pair of numbers which are the sum of each other's proper divisors are called amicable, and larger cycles of numbers are called sociable. A positive integer such that every smaller positive integer is a sum of distinct divisors of it is a practical number.

By definition, a perfect number is a fixed point of the restricted divisor function s(n) = σ(n) − n, and the aliquot sequence associated with a perfect number is a constant sequence</description>
		<content:encoded><![CDATA[<p>The sum of proper divisors gives various other kinds of numbers. Numbers where the sum is less than the number itself are called deficient, and where it is greater than the number, abundant. These terms, together with perfect itself, come from Greek numerology. A pair of numbers which are the sum of each other&#8217;s proper divisors are called amicable, and larger cycles of numbers are called sociable. A positive integer such that every smaller positive integer is a sum of distinct divisors of it is a practical number.</p>
<p>By definition, a perfect number is a fixed point of the restricted divisor function s(n) = σ(n) − n, and the aliquot sequence associated with a perfect number is a constant sequence</p>
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	<item>
		<title>By: Valter</title>
		<link>http://www.liewcf.com/blog/archives/2006/10/free-rapidshare-account-by-solving-a-math-problem/#comment-256487</link>
		<dc:creator>Valter</dc:creator>
		<pubDate>Fri, 09 Feb 2007 22:01:25 +0000</pubDate>
		<guid isPermaLink="false">http://www.liewcf.com/blog/?p=2647#comment-256487</guid>
		<description>the aswer is simple. Its: "none" . Because if sum all digits you only get an s so  s is not a n so theres none</description>
		<content:encoded><![CDATA[<p>the aswer is simple. Its: &#8220;none&#8221; . Because if sum all digits you only get an s so  s is not a n so theres none</p>
]]></content:encoded>
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		<title>By: confucious</title>
		<link>http://www.liewcf.com/blog/archives/2006/10/free-rapidshare-account-by-solving-a-math-problem/#comment-255367</link>
		<dc:creator>confucious</dc:creator>
		<pubDate>Thu, 08 Feb 2007 13:11:34 +0000</pubDate>
		<guid isPermaLink="false">http://www.liewcf.com/blog/?p=2647#comment-255367</guid>
		<description>huh? are you really gonna be using any of these methods. i think its a wast of my time.</description>
		<content:encoded><![CDATA[<p>huh? are you really gonna be using any of these methods. i think its a wast of my time.</p>
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		<title>By: Appzalien</title>
		<link>http://www.liewcf.com/blog/archives/2006/10/free-rapidshare-account-by-solving-a-math-problem/#comment-253899</link>
		<dc:creator>Appzalien</dc:creator>
		<pubDate>Wed, 07 Feb 2007 00:17:23 +0000</pubDate>
		<guid isPermaLink="false">http://www.liewcf.com/blog/?p=2647#comment-253899</guid>
		<description>s/n  if the number of digits is 4 (n) then the total number of digits has to be divisible by 4 or 4,8,12,16 etc and dividing this number (s) by (n) will give you the number.  16/4 = 4 numbers of 4 digits each.</description>
		<content:encoded><![CDATA[<p>s/n  if the number of digits is 4 (n) then the total number of digits has to be divisible by 4 or 4,8,12,16 etc and dividing this number (s) by (n) will give you the number.  16/4 = 4 numbers of 4 digits each.</p>
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		<title>By: Victor</title>
		<link>http://www.liewcf.com/blog/archives/2006/10/free-rapidshare-account-by-solving-a-math-problem/#comment-240755</link>
		<dc:creator>Victor</dc:creator>
		<pubDate>Wed, 24 Jan 2007 11:47:18 +0000</pubDate>
		<guid isPermaLink="false">http://www.liewcf.com/blog/?p=2647#comment-240755</guid>
		<description>How many numbers of 'n' digits exist if the sum of all digits is 's'?
You can say a number as below
                     
x =   sigma    a[i].10^(n-i)
      i = 1 to n

and

s =   sigma    a[i]
      i = 1 to n

since n can be any number as long can you write, so you can find as that number you can found the 'n'.</description>
		<content:encoded><![CDATA[<p>How many numbers of &#8216;n&#8217; digits exist if the sum of all digits is &#8217;s&#8217;?<br />
You can say a number as below</p>
<p>x =   sigma    a[i].10^(n-i)<br />
      i = 1 to n</p>
<p>and</p>
<p>s =   sigma    a[i]<br />
      i = 1 to n</p>
<p>since n can be any number as long can you write, so you can find as that number you can found the &#8216;n&#8217;.</p>
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		<title>By: Ben</title>
		<link>http://www.liewcf.com/blog/archives/2006/10/free-rapidshare-account-by-solving-a-math-problem/#comment-237893</link>
		<dc:creator>Ben</dc:creator>
		<pubDate>Sat, 20 Jan 2007 10:54:36 +0000</pubDate>
		<guid isPermaLink="false">http://www.liewcf.com/blog/?p=2647#comment-237893</guid>
		<description>chang please send me your mail and I will send you my solution since some strings are cutting off parts of the reply. 
thank you.</description>
		<content:encoded><![CDATA[<p>chang please send me your mail and I will send you my solution since some strings are cutting off parts of the reply.<br />
thank you.</p>
]]></content:encoded>
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	<item>
		<title>By: Ben</title>
		<link>http://www.liewcf.com/blog/archives/2006/10/free-rapidshare-account-by-solving-a-math-problem/#comment-237891</link>
		<dc:creator>Ben</dc:creator>
		<pubDate>Sat, 20 Jan 2007 10:51:52 +0000</pubDate>
		<guid isPermaLink="false">http://www.liewcf.com/blog/?p=2647#comment-237891</guid>
		<description>Ok, this is the real first part, sorry about all these repeted posts.


Please note that because of certain problematic strings all of my signs are 'lesser/greater or equal to'.

My friend Chang Yang, you are absolutely correct!
Thank you for pointing out my lack of attention to that very important fact.
You will be happy to know that there is a solution to that as well.

The formula works for s10, then we start to count non valid arrangements of the balls in the boxes.</description>
		<content:encoded><![CDATA[<p>Ok, this is the real first part, sorry about all these repeted posts.</p>
<p>Please note that because of certain problematic strings all of my signs are &#8216;lesser/greater or equal to&#8217;.</p>
<p>My friend Chang Yang, you are absolutely correct!<br />
Thank you for pointing out my lack of attention to that very important fact.<br />
You will be happy to know that there is a solution to that as well.</p>
<p>The formula works for s10, then we start to count non valid arrangements of the balls in the boxes.</p>
]]></content:encoded>
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		<title>By: Ben</title>
		<link>http://www.liewcf.com/blog/archives/2006/10/free-rapidshare-account-by-solving-a-math-problem/#comment-237889</link>
		<dc:creator>Ben</dc:creator>
		<pubDate>Sat, 20 Jan 2007 10:49:53 +0000</pubDate>
		<guid isPermaLink="false">http://www.liewcf.com/blog/?p=2647#comment-237889</guid>
		<description>The top got cut off again, sorry


Please note that because of certain problematic strings all of my &#62; or 10, then we start to count non valid arrangements of the balls in the boxes.</description>
		<content:encoded><![CDATA[<p>The top got cut off again, sorry</p>
<p>Please note that because of certain problematic strings all of my &gt; or 10, then we start to count non valid arrangements of the balls in the boxes.</p>
]]></content:encoded>
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		<title>By: Ben</title>
		<link>http://www.liewcf.com/blog/archives/2006/10/free-rapidshare-account-by-solving-a-math-problem/#comment-237887</link>
		<dc:creator>Ben</dc:creator>
		<pubDate>Sat, 20 Jan 2007 10:47:34 +0000</pubDate>
		<guid isPermaLink="false">http://www.liewcf.com/blog/?p=2647#comment-237887</guid>
		<description>Please note that because of certain problematic strings all of my &#62;10, then we start to count non valid arrangements of the balls in the boxes.

To counter this we must put a restraint on the question itself. This would be whenever s&#62;9 we must make sure that none of the boxes have more that 9 balls.

Before I explain the example let me state that for s 0.

Lets derive m from n and we get that the above equation is now 
(8-m1)+(9-m2)+(9-m3) = 25.

This of course is equivalent to m1+m2+m3 = 1 (26-25) while m1,m2,m3 &#62; 0.

So now the question is how many distributions of 1 ball are there into 3 boxes?
The answer is of course 3 or (3+1-1)C(1) = 3.

We can simply generalize this example to any n &#62;1 and s&#62;10 while we use the same template of (n+s-1)C(s)   and we get the answer of 
(10n-s-1)C(n-1).

So there are 2 answers:
1. When s10: (10n-s-1)C(n-1).

I’m sorry for the lengthy response but I could’ve made it longer :-)
I hope this answers your question. 
Have a wonderful day.</description>
		<content:encoded><![CDATA[<p>Please note that because of certain problematic strings all of my &gt;10, then we start to count non valid arrangements of the balls in the boxes.</p>
<p>To counter this we must put a restraint on the question itself. This would be whenever s&gt;9 we must make sure that none of the boxes have more that 9 balls.</p>
<p>Before I explain the example let me state that for s 0.</p>
<p>Lets derive m from n and we get that the above equation is now<br />
(8-m1)+(9-m2)+(9-m3) = 25.</p>
<p>This of course is equivalent to m1+m2+m3 = 1 (26-25) while m1,m2,m3 &gt; 0.</p>
<p>So now the question is how many distributions of 1 ball are there into 3 boxes?<br />
The answer is of course 3 or (3+1-1)C(1) = 3.</p>
<p>We can simply generalize this example to any n &gt;1 and s&gt;10 while we use the same template of (n+s-1)C(s)   and we get the answer of<br />
(10n-s-1)C(n-1).</p>
<p>So there are 2 answers:<br />
1. When s10: (10n-s-1)C(n-1).</p>
<p>I’m sorry for the lengthy response but I could’ve made it longer <img src='http://www.liewcf.com/blog/wp-includes/images/smilies/icon_smile.gif' alt=':-)' class='wp-smiley' /><br />
I hope this answers your question.<br />
Have a wonderful day.</p>
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	<item>
		<title>By: Chang Yang</title>
		<link>http://www.liewcf.com/blog/archives/2006/10/free-rapidshare-account-by-solving-a-math-problem/#comment-237511</link>
		<dc:creator>Chang Yang</dc:creator>
		<pubDate>Fri, 19 Jan 2007 19:10:36 +0000</pubDate>
		<guid isPermaLink="false">http://www.liewcf.com/blog/?p=2647#comment-237511</guid>
		<description>It was a lengthy and great explanation, Ben, thanks a lot. Actually I got that far into the question, but the problem that I encountered, and I think what you have not considered, is: you can't put more than 9 balls into _any_ box. And that has made this solution of yours useful only for lower value numbers of s. So for questions such as s=26, n=3, the answer is obviously 3 (998, 989, 899) but your answer will turn it into 27C25 which is obviously not 3.</description>
		<content:encoded><![CDATA[<p>It was a lengthy and great explanation, Ben, thanks a lot. Actually I got that far into the question, but the problem that I encountered, and I think what you have not considered, is: you can&#8217;t put more than 9 balls into _any_ box. And that has made this solution of yours useful only for lower value numbers of s. So for questions such as s=26, n=3, the answer is obviously 3 (998, 989, 899) but your answer will turn it into 27C25 which is obviously not 3.</p>
]]></content:encoded>
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	<item>
		<title>By: Ben</title>
		<link>http://www.liewcf.com/blog/archives/2006/10/free-rapidshare-account-by-solving-a-math-problem/#comment-237363</link>
		<dc:creator>Ben</dc:creator>
		<pubDate>Fri, 19 Jan 2007 17:01:28 +0000</pubDate>
		<guid isPermaLink="false">http://www.liewcf.com/blog/?p=2647#comment-237363</guid>
		<description>Lol, sorry again but i see the last part of  my post got cut off. I changed the string abit so now there should be no prob.


6. But this is not the correct answer yet, because if s=5 and n=3 the number 005 is not a valid number and the answer in “5.” counts those numbers. 
So we find that we have to place at least 1 ball in the most left box (meaning the number has to start with at least 1). So now that we have only s-1 balls to divide into n boxes the correct answer is 
(n+(s-1)-1)C(s-1) = (n+s-2)C(s-1)  [remember that s gets s-1].

7. since we are dealing with numbers in base 10, there are certain limitations on what we can ask. For example the answer to s=28, n=3 is 0 since there are no 3 digit numbers that add up to 28 (27 max)
so the answer will not be 0 if and only if 0</description>
		<content:encoded><![CDATA[<p>Lol, sorry again but i see the last part of  my post got cut off. I changed the string abit so now there should be no prob.</p>
<p>6. But this is not the correct answer yet, because if s=5 and n=3 the number 005 is not a valid number and the answer in “5.” counts those numbers.<br />
So we find that we have to place at least 1 ball in the most left box (meaning the number has to start with at least 1). So now that we have only s-1 balls to divide into n boxes the correct answer is<br />
(n+(s-1)-1)C(s-1) = (n+s-2)C(s-1)  [remember that s gets s-1].</p>
<p>7. since we are dealing with numbers in base 10, there are certain limitations on what we can ask. For example the answer to s=28, n=3 is 0 since there are no 3 digit numbers that add up to 28 (27 max)<br />
so the answer will not be 0 if and only if 0</p>
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	<item>
		<title>By: Ben</title>
		<link>http://www.liewcf.com/blog/archives/2006/10/free-rapidshare-account-by-solving-a-math-problem/#comment-237358</link>
		<dc:creator>Ben</dc:creator>
		<pubDate>Fri, 19 Jan 2007 16:58:21 +0000</pubDate>
		<guid isPermaLink="false">http://www.liewcf.com/blog/?p=2647#comment-237358</guid>
		<description>5. Now the number of ways to place ‘s’ exact balls into ‘n’ distinct boxes is (n+s-1)C(s) (never mind why but I would be happy to explain as well).

6. But this is not the correct answer yet, because if s=5 and n=3 the number 005 is not a valid number and the answer in “5.” counts those numbers. 
So we find that we have to place at least 1 ball in the most left box (meaning the number has to start with at least 1). So now that we have only s-1 balls to divide into n boxes the correct answer is 
(n+(s-1)-1)C(s-1) = (n+s-2)C(s-1)  [remember that s </description>
		<content:encoded><![CDATA[<p>5. Now the number of ways to place ‘s’ exact balls into ‘n’ distinct boxes is (n+s-1)C(s) (never mind why but I would be happy to explain as well).</p>
<p>6. But this is not the correct answer yet, because if s=5 and n=3 the number 005 is not a valid number and the answer in “5.” counts those numbers.<br />
So we find that we have to place at least 1 ball in the most left box (meaning the number has to start with at least 1). So now that we have only s-1 balls to divide into n boxes the correct answer is<br />
(n+(s-1)-1)C(s-1) = (n+s-2)C(s-1)  [remember that s</p>
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	<item>
		<title>By: Ben</title>
		<link>http://www.liewcf.com/blog/archives/2006/10/free-rapidshare-account-by-solving-a-math-problem/#comment-237357</link>
		<dc:creator>Ben</dc:creator>
		<pubDate>Fri, 19 Jan 2007 16:58:05 +0000</pubDate>
		<guid isPermaLink="false">http://www.liewcf.com/blog/?p=2647#comment-237357</guid>
		<description>I'm just splitting my reply. sorry

Hi all.

I would just like to put all of you wonderfull thinkers at ease.
First of all DarkAngel is correct and the solution is quit simple. The reason im posting this is to explain (i think the answer needs some explaining) the answer (This is regards to Chang Yangs request).

Think of the question this way:

1. 's' is the sum of the digits of a 'n' long number.

2. So lets pretend that we have ‘n’ different boxes representing the number of digits.

3. Lets also pretend that we have 's' balls that we can divide to those boxes.

4. Now in order to answer the question, we have reduced it to simply asking how many different ways are there to divide the balls to the boxes (NOT DONE YET).

Explanation of 4: 
If you think about this it makes perfect sense, since the sum of the digits can’t exceed the number of balls. So if we were to divide 5 balls to a 3 digit number then the number 113 would be like placing 1 ball in the first and second box and placing 3 balls in the third box.</description>
		<content:encoded><![CDATA[<p>I&#8217;m just splitting my reply. sorry</p>
<p>Hi all.</p>
<p>I would just like to put all of you wonderfull thinkers at ease.<br />
First of all DarkAngel is correct and the solution is quit simple. The reason im posting this is to explain (i think the answer needs some explaining) the answer (This is regards to Chang Yangs request).</p>
<p>Think of the question this way:</p>
<p>1. &#8217;s&#8217; is the sum of the digits of a &#8216;n&#8217; long number.</p>
<p>2. So lets pretend that we have ‘n’ different boxes representing the number of digits.</p>
<p>3. Lets also pretend that we have &#8217;s&#8217; balls that we can divide to those boxes.</p>
<p>4. Now in order to answer the question, we have reduced it to simply asking how many different ways are there to divide the balls to the boxes (NOT DONE YET).</p>
<p>Explanation of 4:<br />
If you think about this it makes perfect sense, since the sum of the digits can’t exceed the number of balls. So if we were to divide 5 balls to a 3 digit number then the number 113 would be like placing 1 ball in the first and second box and placing 3 balls in the third box.</p>
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		<title>By: Ben</title>
		<link>http://www.liewcf.com/blog/archives/2006/10/free-rapidshare-account-by-solving-a-math-problem/#comment-237353</link>
		<dc:creator>Ben</dc:creator>
		<pubDate>Fri, 19 Jan 2007 16:55:12 +0000</pubDate>
		<guid isPermaLink="false">http://www.liewcf.com/blog/?p=2647#comment-237353</guid>
		<description>Hi all.

I would just like to put all of you wonderfull thinkers at ease.
First of all DarkAngel is correct and the solution is quit simple. The reason im posting this is to explain (i think the answer needs some explaining) the answer (This is regards to Chang Yangs request).

Think of the question this way:

1. 's' is the sum of the digits of a 'n' long number.

2. So lets pretend that we have ‘n’ different boxes representing the number of digits.

3. Lets also pretend that we have 's' balls that we can divide to those boxes.

4. Now in order to answer the question, we have reduced it to simply asking how many different ways are there to divide the balls to the boxes (NOT DONE YET).

Explanation of 4: 
If you think about this it makes perfect sense, since the sum of the digits can’t exceed the number of balls. So if we were to divide 5 balls to a 3 digit number then the number 113 would be like placing 1 ball in the first and second box and placing 3 balls in the third box.

5. Now the number of ways to place ‘s’ exact balls into ‘n’ distinct boxes is (n+s-1)C(s) (never mind why but I would be happy to explain as well).

6. But this is not the correct answer yet, because if s=5 and n=3 the number 005 is not a valid number and the answer in “5.” counts those numbers. 
So we find that we have to place at least 1 ball in the most left box (meaning the number has to start with at least 1). So now that we have only s-1 balls to divide into n boxes the correct answer is 
(n+(s-1)-1)C(s-1) = (n+s-2)C(s-1)  [remember that s </description>
		<content:encoded><![CDATA[<p>Hi all.</p>
<p>I would just like to put all of you wonderfull thinkers at ease.<br />
First of all DarkAngel is correct and the solution is quit simple. The reason im posting this is to explain (i think the answer needs some explaining) the answer (This is regards to Chang Yangs request).</p>
<p>Think of the question this way:</p>
<p>1. &#8217;s&#8217; is the sum of the digits of a &#8216;n&#8217; long number.</p>
<p>2. So lets pretend that we have ‘n’ different boxes representing the number of digits.</p>
<p>3. Lets also pretend that we have &#8217;s&#8217; balls that we can divide to those boxes.</p>
<p>4. Now in order to answer the question, we have reduced it to simply asking how many different ways are there to divide the balls to the boxes (NOT DONE YET).</p>
<p>Explanation of 4:<br />
If you think about this it makes perfect sense, since the sum of the digits can’t exceed the number of balls. So if we were to divide 5 balls to a 3 digit number then the number 113 would be like placing 1 ball in the first and second box and placing 3 balls in the third box.</p>
<p>5. Now the number of ways to place ‘s’ exact balls into ‘n’ distinct boxes is (n+s-1)C(s) (never mind why but I would be happy to explain as well).</p>
<p>6. But this is not the correct answer yet, because if s=5 and n=3 the number 005 is not a valid number and the answer in “5.” counts those numbers.<br />
So we find that we have to place at least 1 ball in the most left box (meaning the number has to start with at least 1). So now that we have only s-1 balls to divide into n boxes the correct answer is<br />
(n+(s-1)-1)C(s-1) = (n+s-2)C(s-1)  [remember that s</p>
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