Digital root
=============

Given a natural number, ``n``, its digital root is defined as the
result of adding its digits, and iterating this process with the new
number until you reach a single digit number. This digit is called the
digital root of ``n``. For example,

.. raw:: html

   <center>

:math:`374 \Rightarrow 
3 + 4 + 7 = 14 \Rightarrow 
1 + 4 = 5 \Rightarrow
digital\_root(374) = 5`

.. raw:: html

   </center>

Save all these functions into a file named: ``digitalroot.py``

#. Write function :py:func:`add_digits` that given an integer, ``n``,
   returns the addition of its digits. Examples:
   
   .. literalinclude:: add_digits.txt
         :language: python3
         :lines: 3-

   .. note::
        More tests are provided in file :download:`add_digits.txt <add_digits.txt>`

#. Write function :py:func:`digital_root` that from an integer,
   ``n``, returns its digital root. You must use the previous function
   :py:func:`add_digits`. Examples:

   .. literalinclude:: digital_root.txt
         :language: python3
         :lines: 3-

   .. note::
        More tests are provided in file :download:`digital_root.txt <digital_root.txt>`

#. Write function :py:func:`is_digital_root` that given two
   integers, ``n`` and ``r``, returns ``True`` if ``r`` is the digital
   root of ``n`` or ``False`` otherwise. You must use the previous
   function. Examples:

   .. literalinclude:: is_digital_root.txt
         :language: python3
         :lines: 3-10

   .. note::
        More tests are provided in file :download:`is_digital_root.txt <is_digital_root.txt>`

#. Write function :py:func:`is_partial_add` that given two
   integers, ``n`` and ``p``, returns ``True`` if ``p`` is a partial
   addition obtained during the calculation of the digital root of
   ``n`` or ``False``, otherwise. For example: 5 and 14 are partial
   additions of 374. To write this function you can get inspiration
   from function :py:func:`digital_root`. Examples:

   .. literalinclude:: is_partial_add.txt
         :language: python3
         :lines: 3-10

   .. note::
        More tests are provided in file :download:`is_partial_add.txt <is_partial_add.txt>`

   
.. rubric:: Solution

A solution of these functions is provided in file :download:`digitalroot.py
<solutions/digitalroot.py>`.