This is a generic generating functions problem, and you are left with 1/(x-1)(x^5-1)....(x^50-1) however now I want to find the coefficient of the x^100 term of this expression... how can I do this or do I have to use partial fractions which will take ages...
2026-04-02 19:48:14.1775159294
How many ways can you make change for a dollar?
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See http://www.maa.org/frank-morgans-math-chat-293-ways-to-make-change-for-a-dollar. This site shows how the answer is obtained with just some intelligent counting. Despite the title of the site Frank Morgan suggests $292$ ways, not counting a dollar coin.