Solving Subset Sum Counting: How to Make £2 from Coins

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SUMMARY

The forum discussion centers around solving the Subset Sum Counting problem, specifically determining the number of ways to make £2 using coins of denominations 200, 100, 50, 20, 10, 5, 2, and 1. The user expresses difficulty in finding a viable solution, contemplating both a recursive approach and the potential use of generating functions. The consensus suggests that generating functions may provide a more efficient method for solving this problem compared to brute-force recursion.

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Homework Statement


How many different ways can £2 be made using any number of coins?
(In other words, how many ways can you obtain the sum of 200 with terms from the following finite set - 200, 100, 50, 20, 10, 5, 2, 1. Order does not matter.)

Homework Equations


None?


The Attempt at a Solution


No idea.
I've been mulling over this problem for way too much time now without producing anything viable.
A PnP solution is beyond me at this point. On the computational side I've been thinking of a recursive solution which should spawn this massive recursion tree and I'm pretty sure there's got to be a better method out there.
 
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Do you know generating functions??
 
Nope...
First time I've heard of those. I can always read up on them if they are relevant to the solution.
 

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