project_euler.problem_205.sol1
==============================

.. py:module:: project_euler.problem_205.sol1

.. autoapi-nested-parse::

   Project Euler Problem 205: https://projecteuler.net/problem=205

   Peter has nine four-sided (pyramidal) dice, each with faces numbered 1, 2, 3, 4.
   Colin has six six-sided (cubic) dice, each with faces numbered 1, 2, 3, 4, 5, 6.

   Peter and Colin roll their dice and compare totals: the highest total wins.
   The result is a draw if the totals are equal.

   What is the probability that Pyramidal Peter beats Cubic Colin?
   Give your answer rounded to seven decimal places in the form 0.abcdefg



Functions
---------

.. autoapisummary::

   project_euler.problem_205.sol1.solution
   project_euler.problem_205.sol1.total_frequency_distribution


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

.. py:function:: solution() -> float

   Returns probability that Pyramidal Peter beats Cubic Colin
   rounded to seven decimal places in the form 0.abcdefg

   >>> solution()
   0.5731441


.. py:function:: total_frequency_distribution(sides_number: int, dice_number: int) -> list[int]

   Returns frequency distribution of total

   >>> total_frequency_distribution(sides_number=6, dice_number=1)
   [0, 1, 1, 1, 1, 1, 1]

   >>> total_frequency_distribution(sides_number=4, dice_number=2)
   [0, 0, 1, 2, 3, 4, 3, 2, 1]