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Making Change for a Dollar (and other number partitioning problems)
I am working on the classic coin problem where I would like to calculate the number of ways to make change for a dollar with a given number of denominations. From here, I am also going to be working on how to partition the number 100 with at least two positive integers below 100.
I have read over all the same posts on here and other sites and still I am unsure of what I am doing wrong.
The answer to our problem (293) is the coefficient of x100 in the
reciprocal of the following:
(1−x)(1−x5)(1−x10)(1−x25)(1−x50)(1−x100).
I do out this equation with x=100 and get a really large return. My skills are very limited and most of the sites I have been reading over use terminology and operators/symbols I am unfamiliar with.
I look at this and think it seems very straight forward but, I get answers that way off. Are there any tips or steps that I could be overlooking?