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# Problem 76: Counting summations

(see projecteuler.net/problem=76)

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

4 + 1

3 + 2

3 + 1 + 1

2 + 2 + 1

2 + 1 + 1 + 1

1 + 1 + 1 + 1 + 1

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

# My Algorithm

Only very few adjustments to problem 31:

- replace anything related to coins by the numbers 1..100
- finally subtract 1 because the sum has to consist of at least two numbers (not just one)
- for more details on the algorithm itself, please read my explanation of problem 31

proven code is still the fastest way to solve a problem ...

# Interactive test

You can submit your own input to my program and it will be instantly processed at my server:

This is equivalent to`echo "1 6" | ./76`

Output:

*Note:* the original problem's input `100`

__cannot__ be entered

because just copying results is a soft skill reserved for idiots.

*(this interactive test is still under development, computations will be aborted after one second)*

# My code

… was written in C++11 and can be compiled with G++, Clang++, Visual C++. You can download it, too.

#include