"This question is not devoid of sense, but it serves no useful purpose. It may be solved analytically, but would probably lead to very complicated expressions, that would be of no interest for celestial mechanics. For the second focus is only a constructive addition, that has nothing real in space corresponding to it. What else is troubling you?" "My next difficulty is a little problem that sounds quite simple and yet is sufficiently awkward to make one rack one's brains. It was suggested to me by an engineer who certainly has a keen mind for such things, and yet, as far as I could judge, he did not get a solution for it. It concerns the position of the hands of a clock." "You surely are not referring to the children's puzzle of how often and when both hands coincide in position?" "By no means. As I said just now, it is really quite perplexing. Let us assume the position of the hands at twelve o'clock, when both hands coincide. If they are now interchanged, we still have a possible position of the hands, giving an actual time. But, in another case, say, exactly six o'clock, we get a false position of the hands, if we interchange them, for on a normal clock it is impossible for the large hand to be on the six whilst the small hand is on the twelve. The question is now: When and how often are the two hands situated so that when they are interchanged, the new position gives a possible time on the clock?" "There, you see," said Einstein, "that is just the right kind of distraction for an invalid. It is quite interesting, and not too easy. But I am afraid the pleasure will not be of great duration, for I already see a way to solve it." Supporting himself on his elbow, he sketched a diagram on a sheet of paper that gave a clear picture of the conditions of the problem. I can no longer recollect how he arrived at the terms of his equation. At any rate, the result soon came to hand in a time not much longer than I had taken to enunciate the problem to him. It was a so-called indeterminate (Diophantic) equation between two unknowns, that was to be satisfied by simple integers only. He showed that the desired position of the hands was possible 143 times in 12 hours, an equal interval separating each successive position; that is, starting from twelve o'clock, the two hands may be interchanged every 5 minutes ²⁄₁₄₃ seconds, and yet give a possible time. * * * * * * * *