diff --git a/math_probability/add_digits/__init__.py b/math_probability/add_digits/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/math_probability/add_digits/add_digits_challenge.ipynb b/math_probability/add_digits/add_digits_challenge.ipynb
new file mode 100644
index 0000000..faee03a
--- /dev/null
+++ b/math_probability/add_digits/add_digits_challenge.ipynb
@@ -0,0 +1,176 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Challenge Notebook"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Problem: Given an int, repeatedly add its digits until the result is one digit.\n",
+ "\n",
+ "* [Constraints](#Constraints)\n",
+ "* [Test Cases](#Test-Cases)\n",
+ "* [Algorithm](#Algorithm)\n",
+ "* [Code](#Code)\n",
+ "* [Unit Test](#Unit-Test)\n",
+ "* [Solution Notebook](#Solution-Notebook)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Constraints\n",
+ "\n",
+ "* Can we assume num is not negative?\n",
+ " * Yes\n",
+ "* Can we assume the inputs are valid?\n",
+ " * No\n",
+ "* Can we assume this fits memory?\n",
+ " * Yes"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Test Cases\n",
+ "\n",
+ "\n",
+ "* None input -> TypeError\n",
+ "* negative input -> ValueError\n",
+ "* 9 -> 9\n",
+ "* 138 -> 3\n",
+ "* 65536 -> 7\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Algorithm\n",
+ "\n",
+ "Refer to the [Solution Notebook](). If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Code"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "class Solution(object):\n",
+ "\n",
+ " def add_digits(self, val):\n",
+ " # TODO: Implement me\n",
+ " pass"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Unit Test"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**The following unit test is expected to fail until you solve the challenge.**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "# %load test_add_digits.py\n",
+ "from nose.tools import assert_equal, assert_raises\n",
+ "\n",
+ "\n",
+ "class TestAddDigits(object):\n",
+ "\n",
+ " def test_add_digits(self, func):\n",
+ " assert_raises(TypeError, func, None)\n",
+ " assert_raises(ValueError, func, -1)\n",
+ " assert_equal(func(0), 0)\n",
+ " assert_equal(func(9), 9)\n",
+ " assert_equal(func(138), 3)\n",
+ " assert_equal(func(65536), 7) \n",
+ " print('Success: test_add_digits')\n",
+ "\n",
+ "\n",
+ "def main():\n",
+ " test = TestAddDigits()\n",
+ " solution = Solution()\n",
+ " test.test_add_digits(solution.add_digits)\n",
+ " try:\n",
+ " test.test_add_digits(solution.add_digits_optimized)\n",
+ " except NameError:\n",
+ " # Alternate solutions are only defined\n",
+ " # in the solutions file\n",
+ " pass\n",
+ "\n",
+ "\n",
+ "if __name__ == '__main__':\n",
+ " main()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Solution Notebook\n",
+ "\n",
+ "Review the [Solution Notebook]() for a discussion on algorithms and code solutions."
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.5.0"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/math_probability/add_digits/add_digits_solution.ipynb b/math_probability/add_digits/add_digits_solution.ipynb
new file mode 100644
index 0000000..a0c7781
--- /dev/null
+++ b/math_probability/add_digits/add_digits_solution.ipynb
@@ -0,0 +1,224 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Solution Notebook"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Problem: Given an int, repeatedly add its digits until the result is one digit.\n",
+ "\n",
+ "* [Constraints](#Constraints)\n",
+ "* [Test Cases](#Test-Cases)\n",
+ "* [Algorithm](#Algorithm)\n",
+ "* [Code](#Code)\n",
+ "* [Unit Test](#Unit-Test)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Constraints\n",
+ "\n",
+ "* Can we assume num is not negative?\n",
+ " * Yes\n",
+ "* Can we assume the inputs are valid?\n",
+ " * No\n",
+ "* Can we assume this fits memory?\n",
+ " * Yes"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Test Cases\n",
+ "\n",
+ "\n",
+ "* None input -> TypeError\n",
+ "* negative input -> ValueError\n",
+ "* 9 -> 9\n",
+ "* 138 -> 3\n",
+ "* 65536 -> 7\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Algorithm\n",
+ "\n",
+ "The naive solution simply isolates each digit with with modulo and integer division. We'll add each isolated digit to a list and sum the values.\n",
+ "\n",
+ "\n",
+ "138 % 10 = 8 -> isolated\n",
+ "138 // 10 = 13\n",
+ "13 % 10 = 3 -> isolated\n",
+ "13 // 10 = 1\n",
+ "1 % 10 = 1 -> isolated\n",
+ "
\n",
+ "\n",
+ "A more optimal solution exists, by recognizing this is a digital root. See the [Wikipedia article](https://en.wikipedia.org/wiki/Digital_root) for more information.\n",
+ "\n",
+ "Complexity:\n",
+ "* Time: O(1)\n",
+ "* Space: O(1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Code"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "class Solution(object):\n",
+ "\n",
+ " def add_digits(self, num):\n",
+ " if num is None:\n",
+ " raise TypeError('num cannot be None')\n",
+ " if num < 0:\n",
+ " raise ValueError('num cannot be negative')\n",
+ " digits = []\n",
+ " while num != 0:\n",
+ " digits.append(num % 10)\n",
+ " num //= 10\n",
+ " digits_sum = sum(digits)\n",
+ " if digits_sum >= 10:\n",
+ " return self.add_digits(digits_sum)\n",
+ " else:\n",
+ " return digits_sum\n",
+ "\n",
+ " def add_digits_optimized(self, num):\n",
+ " if num is None:\n",
+ " raise TypeError('num cannot be None')\n",
+ " if num < 0:\n",
+ " raise ValueError('num cannot be negative')\n",
+ " if num == 0:\n",
+ " return 0\n",
+ " elif num % 9 == 0:\n",
+ " return 9\n",
+ " else:\n",
+ " return num % 9"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Unit Test"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Overwriting test_add_digits.py\n"
+ ]
+ }
+ ],
+ "source": [
+ "%%writefile test_add_digits.py\n",
+ "from nose.tools import assert_equal, assert_raises\n",
+ "\n",
+ "\n",
+ "class TestAddDigits(object):\n",
+ "\n",
+ " def test_add_digits(self, func):\n",
+ " assert_raises(TypeError, func, None)\n",
+ " assert_raises(ValueError, func, -1)\n",
+ " assert_equal(func(0), 0)\n",
+ " assert_equal(func(9), 9)\n",
+ " assert_equal(func(138), 3)\n",
+ " assert_equal(func(65536), 7) \n",
+ " print('Success: test_add_digits')\n",
+ "\n",
+ "\n",
+ "def main():\n",
+ " test = TestAddDigits()\n",
+ " solution = Solution()\n",
+ " test.test_add_digits(solution.add_digits)\n",
+ " try:\n",
+ " test.test_add_digits(solution.add_digits_optimized)\n",
+ " except NameError:\n",
+ " # Alternate solutions are only defined\n",
+ " # in the solutions file\n",
+ " pass\n",
+ "\n",
+ "\n",
+ "if __name__ == '__main__':\n",
+ " main()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Success: test_add_digits\n",
+ "Success: test_add_digits\n"
+ ]
+ }
+ ],
+ "source": [
+ "%run -i test_add_digits.py"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.4.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/math_probability/add_digits/test_add_digits.py b/math_probability/add_digits/test_add_digits.py
new file mode 100644
index 0000000..dd3d289
--- /dev/null
+++ b/math_probability/add_digits/test_add_digits.py
@@ -0,0 +1,29 @@
+from nose.tools import assert_equal, assert_raises
+
+
+class TestAddDigits(object):
+
+ def test_add_digits(self, func):
+ assert_raises(TypeError, func, None)
+ assert_raises(ValueError, func, -1)
+ assert_equal(func(0), 0)
+ assert_equal(func(9), 9)
+ assert_equal(func(138), 3)
+ assert_equal(func(65536), 7)
+ print('Success: test_add_digits')
+
+
+def main():
+ test = TestAddDigits()
+ solution = Solution()
+ test.test_add_digits(solution.add_digits)
+ try:
+ test.test_add_digits(solution.add_digits_optimized)
+ except NameError:
+ # Alternate solutions are only defined
+ # in the solutions file
+ pass
+
+
+if __name__ == '__main__':
+ main()
\ No newline at end of file