The "Enrichment Program for Cultivating Problem Solving Abilities and Multiple Intelligences for Gifted Preschoolers" (PSMIGP program) was the first enrichment program for young gifted children in Taiwan. It was an extra-curricular program that was implemented over a 3-year period. The assessment and curriculum were designed by adapting the main part of the DISCOVER curriculum. The purpose of this paper was to introduce the identification model and to analyze the participants' performance in problem solving activities and in demonstrating their special talents. To offer enrichment services for gifted young children, the researchers developed an identification model to discover more young gifted children and serve their needs in learning, regardless of the nature of their talents, disabilities, or cultural or socio-economical status. All participating young children were screened in a three-stage process that included both objective and subjective assessments, including checklists, interviews, portfolio assessment, group intelligence tests, observation in the play corner, individual intelligence tests, and structured observation activities. It was also necessary to adjust the standardized test procedure to fit the needs of twice exceptional young children. In total there were sixty-one preschoolers participated in this three-year program, including eleven twice exceptional children and one child from a new immigrant home. Among these sixty-one preschoolers, eight of them participated in two years of the program; the others only participated in one year of the program. The results of this enrichment program found significant correlations among the measurement scores; the scores of teacher assessment of problem solving abilities also showed that most students performed well on all five kinds of problem solving types. From children's archives, participating children presented scientific thinking characteristics, such as rich knowledge with fascinating imagination and the ability to seek many approaches to solving problems. They were delighted to challenge others and pleased to be challenged. The twice exceptional children also performed well in the program, especially those children with autism whose progress in social skills and group adaptability were remarkable. In sum, the researchers in this program had a belief that children, whether gifted or not, did not get the satisfaction of making progress until they had opportunities to find and develop their potentials. (Contains 11 figures and 8 tables.)