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Counting Summations

 Published on Friday, 13th August 2004, 06:00 pm; Solved by 30568;
Difficulty rating: 10%

Problem 76

It is possible to write five as a sum in exactly six different ways:

\begin{align} &4 + 1\\ &3 + 2\\ &3 + 1 + 1\\ &2 + 2 + 1\\ &2 + 1 + 1 + 1\\ &1 + 1 + 1 + 1 + 1 \end{align}

How many different ways can one hundred be written as a sum of at least two positive integers?