Would a child who hasn't learned what order the numerals go in be able to tell someone their age?

Yes.  The reason is because they don't have to be able to count to be able to repeat something like "I am two" or I am three" when someone asks "how old are you".

All that needs to happen is for someone to tell them "you are three years old" often enough that if someone asks "how old are you" - the response is "three years old".

But - some toddlers do also still get their age wrong because they just don't repeat things well.  (Or a child that has recently turned three will still insist that they are "two".)

Yes.

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