You can never write a class without a toString$()$ method, because:

if you do not put a toString$()$ in your class, one will be inherited from the class named Exception.

if you do not put a toString$()$ in your class, the compiler will place one for you in your class.

if you do not put a toString$()$ in your class, the Java Virtual Machine will make one for you.

if you do not put a toString$()$ in your class, one will be inherited from the class named Object