Geometric means are confusing to a lot of ppl (i had to look it
   up myself to remind myself of what it was) because I don't think
   they teach it in school, which is a shame because it's
   _actually_ very useful.This is geometric mean from an economic
   POV which might help clarify for your
   programmer.[1]http://www.investopedia.com/terms/g/geometricmean.aspHow
   you can analogize it to the clock graph:"Geometric mean" works
   with "percentages of the whole" and doesn't really care about
   the numbers themselves.In my mind it's "percentage away from"
   within a system or, which one is closer relative to another.
   It's a relativistic system rather than an absolute system and
   like all things relativity, is confusing because relativity+math
   don't usually show up together much in school (not much beyond >
   and < ) - until you get into investing and business and you want
   to know thing like ROI and such. ==
   You're working with a set of [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
   12] arranged in a circle.The 12 + 6 are at opposite sides of
   each other.So if you find yourself with a 9 or a 3, they are
   equivalently distant from the 12 and the 6.It is like paper
   folding. Yes, I think in this case your description of "how to
   solve it" works for this situation, although it's a hack
   specific to this model because it fixes the set of 1-12 arranged
   on a clock face. But yes, it can work as long as someone doesn't
   want to use different clocks with different sets of numbers like
   emoticon
   ==
   [and I just realized what *I* said is probably "not quite the
   right way" to explain it either tongue emoticon I can visualize
   in my head what you're trying to do but an explanation *is*
   rather tricky tongue emoticon ]
   ==
   *You're welcome Scott smile emoticon If I was faced with this
   problem, I would probably solve it exactly the same way, but
   include a BIG NOTE in the beginning of the program or
   documentation warning that THIS DOES NOT SCALE.
   ==
   *Yes. Actually, considering the 12/6 are at 180 degrees of each
   other, and the numbers on the face are equally spaced apart...
   ...you could do max / 2 to get your 1/2 way mark rather than
   fixing it at 6.
   ==
   Yeah. I mean scalability is probably not a real issue: I always
   think bigger than is necessary. I think the problem your
   programmer is having is visualizing geometric mean.
   ==
   *It took me a few moments for "what is geometric mean?" to
   "click in" for myself when you mentioned it. I had to look it up
   and then i was like, OOOOH, that's right.
   ==

References

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   1. http://l.facebook.com/l.php?u=http%3A%2F%2Fwww.investopedia.com%2Fterms%2Fg%2Fgeometricmean.asp&h=8AQGW5H7X