The rule holds across the whole class Chilopoda. Counts run from 15 pairs in house centipedes and stone centipedes up to 191 pairs in some soil centipedes, and every recorded number in between is odd. The developmental basis appears to lie in how segments are added in pairs during embryogenesis from an initial odd-numbered set, though the mechanism is not fully explained.
Soil centipedes are where the variation lives. Within a single species the count can differ between individuals, and in many geophilomorphs females carry more leg pairs than males. That intraspecific variability makes them the group where the odd-number constraint is most striking, since the number is not fixed even within a species.
One consequence is that the name is arithmetically impossible. A centipede cannot have 100 legs, because that would require 50 leg-bearing segments, an even number. The nearest counts are 49 pairs, which is 98 legs, and 51 pairs, which is 102.