Problems that ask for an example with prescribed properties, or for a proof that none exists. Examples of such answers: the quaternion group \(Q_8\) is nonabelian and every subgroup of \(Q_8\) is normal; the ideal \((x)\) of \(\ZZ[x]\) is prime and not maximal, since \(\ZZ[x]/(x)\cong\ZZ\); \(\QQ\) is a torsion-free \(\ZZ\)-module that is not free; and the function equal to \(x\) on \(\QQ\) and to \(0\) on \(\RR\setminus\QQ\) is continuous at \(0\) and at no other point, and differentiable at no point.