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by Shane Emmons

Write a program that tells whether a given integer is happy. A happy number is
found using the following process: Take the sum of the squares of its digits,
and continue iterating this process until it yields 1, or produces an infinite
loop.

For example the number 7:

7^2 = 49
4^2 + 9^2 = 97
9^2 + 7^2 = 130
1^2 + 3^2 + 0^2 = 10
1^2 + 0^2 = 1

If a number is not happy than it is obviously unhappy. Now that you have this
program, what is the largest happy number you can find? What is the happiest
number between 1 and 1,000,000. I define the happiest number as the smallest
number that finds the most other happy numbers with it, i.e. 7 found four other
numbers (49, 97, 130, and 10) making it a rank 4 in happiness.

If you find all these examples trivial, write you program so that it will find
happy numbers in other bases such as base 2 or 16. From there you can extend the
program so that it finds happy bases (other than 2 and 4). A happy bases is a
base where all numbers are happy. Good luck.