I think the real problem with the fizzbuzz example is that the "clever" solution fails to properly break the problem down. Fizz buzz essentially consists of two

I think the real problem with the fizzbuzz example is that the "clever" solution fails to properly break the problem down. Fizz buzz essentially consists of two parts: 1. We have an increasing sequence of numbers. 2. Every number divisible by 3 is replaced with "fizz", every number divisible by 5 is replaced with "buzz", every number divisible by both is replaced with "fizzbuzz". If you set out to solve these two parts individually, you would never come up with the clever solution. While the desired result of fizzbuzz is a specific sequence of numbers, that fact is almost incidental. The clever solution doesn't really look at the problem definition but instead merely generates the desired sequence.