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From ProjectEuler.net:
Prob 76: How many different ways can one hundred be written as a sum of at least two positive integers?
I have no idea how to start this…any points in the right direction or help? I’m not looking for how to do it but some hints on how to do it.
For example 5 can be written like:
4 + 1 3 + 2 3 + 1 + 1 2 + 2 + 1 2 + 1 + 1 + 1 1 + 1 + 1 + 1 + 1 So 6 possibilities total.
Partition Numbers (or Partition Functions) are the key to this one.
Problems like these are usually easier if you start at the bottom and work your way up to see if you can detect any patterns.
Hint: See if you can build P(N) up from some combination of the results prior to P(N).