  Let A be a connected left artinian ring with radical square zero and with n
simple modules. If A is not self-injective, then we show that any module M with
Ext^i(M,A) = 0 for 1 \le i \le n + 1 is projective. We also determine the
structure of the artin algebras with radical square zero and n simple modules
which have a non-projective module M such that Ext^i(M,A) = 0 for 1 \le i \le
n.
