List a number of ideas to tackle the implementation of FizzBuzz

Author: dvberkel

Ideas.md

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+# Ideas
+
+This document list various ideas on tackling the implementation of FizzBuzz.
+Since some of these ideas are orthogonal, we can rely on a multiplication
+effect to increase the number of options
+
+## Divisibilty
+The essence of the FizzBuzz game is divisibility. There are various different
+ways to determine, what is effectively, the equivalence class of a certain
+number with respect to the modulus.
+
+### `mod`
+The standard implementation used the `mod` function that determines the modulus
+of a number.
+
+### Representation with different Radix
+When the last digit of a representation of a number in a different radix is
+zero that number is divible by the radix.
+
+### Unrolling the loop
+Knowing the remainder after division of 15 is all you need to determine the
+action you need to take. You could use the following table
+
+| Remainder | Result     |
+|-----------|------------|
+| 0         | "FizzBuzz" |
+| 1         | "n"        |
+| 2         | "n"        |
+| 3         | "Fizz"     |
+| 4         | "n"        |
+| 5         | "Buzz"     |
+| 6         | "Fizz"     |
+| 7         | "n"        |
+| 8         | "n"        |
+| 9         | "Fizz"     |
+| 10        | "Buzz"     |
+| 11        | "n"        |
+| 12        | "Fizz"     |
+| 13        | "n"        |
+| 14        | "n"        |
+
+Where `"n"` represents the String representation of the subject under test.
+
+This technique can be applied to various ways of looking up the result
+depending on the remainder. E.g. using a switch expression, using a map for the
+lookup.
+
+### Casting out 9
+There is a "well-know" calculation aid called casting out nines. This allows a
+(human) computer to check if a result is plausible. In effect it can determine
+if a number is divisible by nine.
+
+The crux for decimal number (base 10) is that 10 = 9 + 1. There is a similar
+test for divisibility of 11, which hinges on the fact that 10 = 11 - 1.
+
+By inspecting the binary representation one can devise a similar test because
+2 = 3 - 1 and 2^2 = 4 = 5 - 1.
+
+Details will be in the presentation
+
+## Technology
+There are various other means then flat out implement the algorithm. Below are
+a few suggestions
+
+### SQL
+One could query an prepared structured database.
+
+### Knowledge System
+One could query an knowledge system, like Prolog.
+
+### Machine learning
+One could train an machine to pick out the FizzBuzzyness of numbers.