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### Re^2: How to generate restricted partitions of an integer

by borisz (Canon)
 on Nov 11, 2004 at 13:31 UTC ( #407030=note: print w/replies, xml ) Need Help??

No, I search for distinct combinations only. So I can exchange 100e only one into another 100e.
Boris
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Re^3: How to generate restricted partitions of an integer
by jdporter (Canon) on Nov 11, 2004 at 14:29 UTC
Well, you did say "how often", which is probably a pretty stupid way of phrasing the problem. It certainly led me to think that the problem involved repeated changings, e.g. once I've broken it into two 50s, what can I do with the two 50s. It now seems that you meant to say "How many ways", rather than "How often". I mean, how often? Once per day? Twice per second?

And how would you phrase the question in Russian?

Sorry, I can not express it any better. Look at the example please. The answer, 50 is correct. I think 'How many ways' is good. Just search for any combination of 100, 50, 20 , 10 and 5 euro notes where the sum is 100 without repeating a combination. I hope it is clearer to you now.
Boris
Okay...now I understand the problem. If I dust of my math degree...I think this could be solved with generating functions. Basically, calculate (x+ x**5+ x**10 + x**20 + x**50 + x**100)**100 and find the coeffieient of x**100 in the resulting polynomial. Easy...;)

thor

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