Why not elevenst, twelvend, and thirteenrd?
Solution 1:
It does not depend on whether the ones digit is a 1, 2, or 3; it depends on whether the number is pronounced with a "one", "two", or "three" at the end. Eleven, twelve, and thirteen do not meet the pronunciation criterion and thus get lumped in with the rest of the "regular" numbers.
(Why they're called eleven, twelve, and thirteen instead of oneteen, twoteen, and threeteen is a completely different question....)