Things like Euclid's algorithm, or sorting algorithms, or travelling salesman problem algorithms. Or algorithms to solve Sudku.
The space of all possible algorithms is huge. So is it a case of a million people each trying something different until something works?
On the other hand most people can seem to work out algorithms for solving simple Sudoku's. Yet not everyone can work out algorithms for solving harder Sudoku's yet some people have found many tricks and techniques.