It is not clear that I am entitled to present this paper. For the problem of choice which concerns me was constructed by someone else, and I am not satisfied with my attempts to work through the problem. But since I believe that tho problem will interest and intrigue Peter Hempel and his many friends, and since its publication may call forth a sotution which will enable me to stop returning, periodically, to it, here it is. It was constructed by a physicist, Dr. William Newcomb, of the Livermore Radiation Laboratories in California. I first heard the problem, in 1963, from his friend Professor Martin David Kruskal of the Princeton University Depaftment of Astrophysical sciences. I have benefitted from discussions, in 1963, with William Newcomb, Martin David Kruskal, and Paul Benacerraf. since then, on and off, I have discussed the problem with many other friends whose attempts to grapple with it have encouraged me to publish my own. It is a beautiful problem. I wish it were mine.