We studied the development of cognitive abilities related to intelligence and creativity (N = 48, 6–10 years old), using a longitudinal design (over one school year), in order to evaluate an Enrichment Program for gifted primary school children initiated by the government of the German federal state of Rhineland-Palatinate (Entdeckertag Rheinland Pfalz, Germany; ET; Day of Discoverers). A group of German primary school children (N = 24), identified earlier as intellectually gifted and selected to join the ET program was compared to a gender-, class- and IQ- matched group of control children that did not participate in this program. All participants performed the Standard Progressive Matrices (SPM) test, which measures intelligence in well-defined problem space; the Creative Reasoning Task (CRT), which measures intelligence in ill-defined problem space; and the test of creative thinking-drawing production (TCT-DP), which measures creativity, also in ill-defined problem space. Results revealed that problem space matters: the ET program is effective only for the improvement of intelligence operating in well-defined problem space. An effect was found for intelligence as measured by SPM only, but neither for intelligence operating in ill-defined problem space (CRT) nor for creativity (TCT-DP). This suggests that, depending on the type of problem spaces presented, different cognitive abilities are elicited in the same child. Therefore, enrichment programs for gifted, but also for children attending traditional schools, should provide opportunities to develop cognitive abilities related to intelligence, operating in both well- and ill-defined problem spaces, and to creativity in a parallel, using an interactive approach.