# Name Age
1 Drew youngest
2 Blake next to youngest
3 Alex next to oldest
4 Hayden oldest
If we label the clues:
C1: Hayden was fourth.
C2: Alex was not the oldest, but was older than Drew, who was not second.
C3: The child who was next in age to the youngest, finished second.
C4: The child who finished in third place was older than the child who finished first.
C5: Blake was younger than the child who finished in third place.
Using C2 Alex was not the oldest.
Using C2 Drew was not the oldest.
Using C5 Blake was not the oldest.
Therefore Hayden was the oldest (and using C1 came fourth).
Using C4 the youngest didn't come third, and using C3 the youngest didn't come second.
Therefore the youngest came first.
Using C3 the next to youngest came second, leaving the next to oldest in third.
Using C2 since Drew wasn't second (nor fourth), and Alex was older than Drew, Drew must have come in first.
Using C5 Blake didn't come third, so came second.
Leaving Alex in third.