Separate Sizes or Continuation
It would seem to be sensible to have a single size numbering system for both adults and children. This is the case for some systems with the European, Japanese and Mondopoint systems having a numbering system that allows children's sizes to be smaller numbers in the same system.
The British sizing system, with its roots in the middle ages, has a separate set of sizes for children. This system was used as the basis for both the American and Australian systems and they in turn have separate children's sizes.
Numbering For Children's Sizes
The British, American and Australian numbering systems for children's shoes starts at 1 and goes up to a 13½ after which comes the adult mens size 1. Thus the smaller ladies' sizes will be the same size as the largest children's sizes. In Britain this will lead to the smallest ladies' sizes not being used as children's shoes are free from VAT (Sales Tax).
Mondopoint children's sizes range from about 100 to 200. Similarly Japanese chldren's shoes range from about a size 10 to a size 20. European children's sizes range from about a size 15 to a size 32. It should be remembered that each of these systems does not use a separate numbering system.