1. Leave 6 adjacent numbers of the face of a clock intact and rearrange the other 6 in such a way that the sum of every pair of adjacent numbers is prime.
2. Leave as many numbers as possible in their correct positions on the face of a clock and rearrange the rest such that the sum of every pair of adjacent numbers is prime.
3. Repeat the previous problem, such that the sum of every adjacent pair is composite (not prime).

Source: A small book called Problematical Recreations shown to me by Bill Cleveland. Used as Ken's POTD 3/7/94.