A Question Without an Answer

http://books.google.com/books?id=ysACAAAAMAAJ&pg=PT2&dq=%22sam+loyd%22&as_brr=1&ei=hyxhSYhfpMYyhryR0QE#PPT2,M1

In 1905, the Ingersoll company engaged Sam Loyd to invent a puzzle to promote its new dollar watch. Loyd sent the illustration above and asked:

How soon will the hour, minute and second hands again appear equal distances apart?

The company advertised the puzzle in Scribner’s in June, promising a free watch to the first 10,000 correct respondents. “The full problem is stated above,” the ad ran, “and no further information can be given in fairness to all contestants.” Further, it said, Loyd’s solution “is locked in our safe, inaccessible to any one.”

Perhaps it still is — I can’t find any record of a solution to the puzzle. I offer it here for what it’s worth.