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 ide
A good way to approach these is not get fixated on the '100' but try to consider what the difference between totalling for a sum n and n+1 would be, by looking for patterns as n increases 1,2,3....
I'd have a go now but I have work to do :)