According to the minimum interaction theory, the chromosome evolution of eukaryotes proceeds as a whole toward increasing the chromosome number. This raises the following two questions: what was the starting chromosome number of eukaryotes and does the chromosome number increase infinitely? We attempted to provide a theoretical framework to resolve these questions. We propose that the species with n=2 observed in Protozoa, Platyhelminthes, Annelid, Algae, Fungi and higher plants would be chromosomal relicts conserving the karyotypes of ancestral eukaryotes. We also propose that the ideal highest number of eukaryotes (n(max)) can be given by an inverse of the minimum terminal interference distance (It(min)) in crossing-over (n(max)=100/It(min)). AsIt(min) =0.6 in mammals, n(max) approximately 166. On the other hand, the value estimated by computer simulations is somewhat lower with n(max)=133-138. Our arguments can be applied to other eukaryotes, if they have a localized centromere and the ratio of total synaptonemal complex/nuclear volume is comparable to that of mammals. We revealed that the index of gene shuffling per karyotypes (G) by means of the total number of gamete types with different gene combinations can be formulated asG =2(n+Fxi), where Fxi means interstitial chiasma frequency per cell corresponding to crossing-over mediated by the recombination nodule. The Fxi value increases in proportion to the n value in areas where n<40, but decreases gradually when n>40 and becomes zero when n>83. Therefore, in the ultimate karyotype with n(max)=166, FXi=0 andG =2(n)=2(166), where gene shuffling is guaranteed by the random orientation of chromosomes at the equatorial plate of meiotic metaphase I.