The gracious Bob Mrotek often takes the time to keep me informed of mathematical curiosities that show up on the web that I might have missed, for which I am truly grateful.

Recently he sent me a picture of a clock in which each hour was represented by a mathematical relationship involving three nines. This is similar to the four-fours type of problem that teachers often use, about which I gave some history here.

Bob informed me that the choice of three nines comes from the fact that the group which had the clock face designed were members of the "Triple Nine Society"...a group that consists of the members that score at or above the 99.9th percentile on IQ tests". (The fact that Bob is aware of this little piece of information tells me that he obviously runs with much higher intellectual group than I.)

I will save the Society's clock for last, as a spoiler to a mild puzzle. Bob had sent me the clock because he first noticed a "copy" of the clock, obviously not from the same group. Which contains a mistake. It reminded me of questions I used to test (torture) my advanced math students with in which I would write several expressions of which one was NOT true; then sing the little ditty from Sesame Street,

"One of these things is not like the others, which one isn't the same?"

Well, this clock that Bob sent me has twelve expressions that demonstrate the hour, but one of them is "not like the others." It has an error. Time yourself, how long does it take to find the error.

Here is the "copy"

If you need a hint, or to confirm your solution, the true Triple Nine Society clock is below. Check and see if the one you thought was wrong is right on this one.

And Thanks again to Bob Mrotek for the heads-up.