Added some problems to Numbers

Author: Karan Goel

Numbers/README.md

@@ -30,3 +30,11 @@ Numbers
 **Tax Calculator** - Asks the user to enter a cost and either a country or state tax. It then returns the tax plus the total cost with tax.
 
 **Dijkstra’s Algorithm** - Create a program that finds the shortest path through a graph using its edges.
+
+**Factorial Finder** - The Factorial of a positive integer, n, is defined as the product of the sequence n, n-1, n-2, ...1 and the factorial of zero, 0, is defined as being 1. Solve this using both loops and recursion.
+
+**Complex Number Algebra** - Show addition, multiplication, negation, and inversion of complex numbers in separate functions. (Subtraction and division operations can be made with pairs of these operations.) Print the results for each operation tested.
+
+**Happy Numbers** - A happy number is defined by the following process. Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers, while those that do not end in 1 are unhappy numbers. Display an example of your output here. Find first 8 happy numbers.
+
+**Number Names** - Show how to spell out a number in English. You can use a preexisting implementation or roll your own, but you should support inputs up to at least one million (or the maximum value of your language's default bounded integer type, if that's less). *Optional: Support for inputs other than positive integers (like zero, negative integers, and floating-point numbers).*

README-scratch.md

@@ -34,6 +34,14 @@ Numbers
 
 **Dijkstra’s Algorithm** - Create a program that finds the shortest path through a graph using its edges.
 
+**Factorial Finder** - The Factorial of a positive integer, n, is defined as the product of the sequence n, n-1, n-2, ...1 and the factorial of zero, 0, is defined as being 1. Solve this using both loops and recursion.
+
+**Complex Number Algebra** - Show addition, multiplication, negation, and inversion of complex numbers in separate functions. (Subtraction and division operations can be made with pairs of these operations.) Print the results for each operation tested.
+
+**Happy Numbers** - A happy number is defined by the following process. Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers, while those that do not end in 1 are unhappy numbers. Display an example of your output here. Find first 8 happy numbers.
+
+**Number Names** - Show how to spell out a number in English. You can use a preexisting implementation or roll your own, but you should support inputs up to at least one million (or the maximum value of your language's default bounded integer type, if that's less). *Optional: Support for inputs other than positive integers (like zero, negative integers, and floating-point numbers).*
+
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README.md

@@ -63,6 +63,14 @@ Numbers
 
 **Dijkstra’s Algorithm** - Create a program that finds the shortest path through a graph using its edges.
 
+**Factorial Finder** - The Factorial of a positive integer, n, is defined as the product of the sequence n, n-1, n-2, ...1 and the factorial of zero, 0, is defined as being 1. Solve this using both loops and recursion.
+
+**Complex Number Algebra** - Show addition, multiplication, negation, and inversion of complex numbers in separate functions. (Subtraction and division operations can be made with pairs of these operations.) Print the results for each operation tested.
+
+**Happy Numbers** - A happy number is defined by the following process. Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers, while those that do not end in 1 are unhappy numbers. Display an example of your output here. Find first 8 happy numbers.
+
+**Number Names** - Show how to spell out a number in English. You can use a preexisting implementation or roll your own, but you should support inputs up to at least one million (or the maximum value of your language's default bounded integer type, if that's less). *Optional: Support for inputs other than positive integers (like zero, negative integers, and floating-point numbers).*
+
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@@ -219,3 +227,4 @@ Sources
 =======
 
 [Martyr2’s Mega Project List](http://www.dreamincode.net/forums/topic/78802-martyr2s-mega-project-ideas-list/)
+[Rosetta Code](http://rosettacode.org/)