This paper presents Automatic Algorithm Discoverer (AAD), an evolutionary framework for synthesizing programs of high complexity. To guide evolution, prior evolutionary algorithms have depended on fitness (objective) functions, which are challenging to design. To make evolutionary progress, instead, AAD employs Problem Guided Evolution (PGE), which requires introduction of a group of problems together. With PGE, solutions discovered for simpler problems are used to solve more complex problems in the same group. PGE also enables several new evolutionary strategies, and naturally yields to High-Performance Computing (HPC) techniques. We find that PGE and related evolutionary strategies enable AAD to discover algorithms of similar or higher complexity relative to the state-of-the-art. Specifically, AAD produces Python code for 29 array/vector problems ranging from min, max, reverse, to more challenging problems like sorting and matrix-vector multiplication. Additionally, we find that AAD shows adaptability to constrained environments/inputs and demonstrates outside-of-the-box problem solving abilities.