Solution
= Solution
For $1\leq t\leq|\Omega|$, a group is <sharply t-transitive> when any two ordered $t$-tuples of distinct points are related by exactly one group element. Equivalently its action on the set of such tuples is regular. In the finite case
$$
\boxed{|G|=n(n-1)\cdots(n-t+1),}
$$
and the <stabilizer subgroup> of an ordered $t$-tuple is trivial. The condition includes both existence and uniqueness, not just transitivity.