Analogical reasoning is one of the most complex cognitive functions in humans that allows abstract thinking, high-level reasoning, and learning. Based on analogical reasoning, one can extract an abstract and general concept (i.e., an analogy schema) from a familiar situation and apply it to a new context or domain (i.e., analogy transfer). These processes allow us to solve problems we never encountered before and generate new ideas. However, the place of analogy transfer in problem solving mechanisms is unclear. This presentation will describe several experiments with three main findings. First, we show how analogy transfer facilitates problem-solving, replicating existing empirical data largely based on the radiation/fortress problems with four new riddles. Second, we propose a new experimental task that allows us to quantify analogy transfer. Finally, using science network methodology, we show how restructuring the mental representation of a problem can predict successful solving of an analogous problem. These results shed new light on the cognitive mechanism underlying solution transfer by analogy and provide a new tool to quantify individual abilities.