You want someone that can easily talk about the pros & cons of using different data structures or algorithms to solve problems. Who can move up & down layers of abstraction without getting confused & lost. Who can hide complexity to make clean, readable, maintainable code.
Many people, especially junior/less experienced engineers, have only memorized solutions to problems. They don't have a strong toolbox of solutions and the experience to know how to apply them (and evaluate the options).
A good problem solver is methodical - they don't just guess at random data structures, they identify what the requirements are of the problem and then choose the appropriate data structure (or compose one) which meets those requirements. They'll have a process, which may be different than your process, that they use to break down problems into smaller, solvable pieces.