This thread is taking an ususual turn from expensive letters to odd clocks!
At my age, I cannot remember what I had for breakfast, so, when I saw what I recognized as a 24-hour clock, I just made a comment about seeing them in the Army. I have not seen one since.
I did not analize the position of the numbers or the length of the hands. Now I realize the difference when it is mentioned. Do you know the answer to the riddle, or are you looking for the answer?
At the risk of looking stupid again (a common situation for me), I never felt I could glance at a 24-hour clock and know the time without thinking about it and reading the numbers. (In two years, I never thought about 24-hour time without "translating" into civilian AM and PM time.) If others have that same limitation, it would not make any difference where the numbers are.
Still, if someone offered a 12-hour clock with numbers located out of the traditional positions, I can understand the problem that would create in using it in the normal "glance" fashion. I prefer a watch with traditional hands over a digital for the reason that I do not have to "read" the numbers to get a feel for the time.
Knowing the nature of kwill1911's interests, I suspect there is more to this story. kwill1911, please tell us more.