project_euler.problem_076.sol1
==============================

.. py:module:: project_euler.problem_076.sol1

.. autoapi-nested-parse::

   Counting Summations
   Problem 76: https://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?



Functions
---------

.. autoapisummary::

   project_euler.problem_076.sol1.solution


Module Contents
---------------

.. py:function:: solution(m: int = 100) -> int

   Returns the number of different ways the number m can be written as a
   sum of at least two positive integers.

   >>> solution(100)
   190569291
   >>> solution(50)
   204225
   >>> solution(30)
   5603
   >>> solution(10)
   41
   >>> solution(5)
   6
   >>> solution(3)
   2
   >>> solution(2)
   1
   >>> solution(1)
   0