Based on the combined method in Chinese ancient I-Ching and theory of Taiji, this paper presents the Neutrosophic combinatorics by means of the combinations of the truth, the falsehood, and the indeterminacy in Smarandache’s Neutrosophy. For the Neutrosophic combinatorics we can say that “Changes originate in the Taiji; from the Taiji come the 3 spheres. From the 3 spheres come the 9 elements, and from the 9 elements come the 27 diagrams.” As the application examples, discussing the further revision to Gödel's Incompleteness Theorem; Based on one divides into two, three, more than three, pointing out that one can divide into the mixed fraction parts even hypercomplex numbers parts, such as one divides into two point five parts, one divides into (1+9i+25000j+1700k) parts; By using Neutrosophic combinatorics, also presents the digitized Taiji figure, fractal Taiji figure and the special digitized Taiji figure (one kind of asymmetry Taiji figure). Finally, discussing the rule in the application of Neutrosophic combinatorics, namely the truth uniqueness, for example, if considering that the principle of conservation of energy is a truth, then the principle of conservation of momentum or the principle of conservation of angular momentum no longer can be considered as a truth.
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