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Interesting stuff, Georg ... I have always thought of myself as more of a "flash" thinker than a grinder ... which state of affairs I daily rue. I truly envy those who can sit down and grind out a solution to a problem through the application of formal rules - one of the reasons abstract, but highly formalized (such as calculus, topology, etc.) subjects have been a struggle for me.

I tend to either see it at once, or not at all (or at least only after a long and painful cogitative process).

In the examples given in the article you reference, I got the "BC 544" implication instantly - in fact, I re-read it a couple of times looking for the "hook" that I felt I must have missed. Surely there was something a little less obvious than the BC ...?

With regard to the other (Bob and his Dad and their ages), I would take issue with the author that no creativity or innovation was required to solve it. I assume one could set up some sort of formulaic approach that would provide the answer after a certain amount of computation, but here is the approach my mind took:

Since the only two numbers given were 3 and 4 (Dad is currently three times as old as Bob, and was 4 times as old 4 years ago) it seemed pretty clear that Dad's age was something easily factorable by both 3 and 4 (not a given, I grant you, but a reasonable assumption). Which led me to 12 [no - Dad couldn't be 12], 24 [possible but a quick mental calculation ruled it out, (24 - 4)does NOT equal 4 X (8 - 4)], and 36 - AHA! ... (36 -4) does indeed equal 4 X (12 - 4).

There will be, of course, those who claim this last was a product of pure mathematical ratiocination, but I assure you it was not ... or at least if it was, I was totally unaware of any but the most basic "math-izing". It was more a product of seeing relationships, or something like that. If you ask me to present the above reasoning in something resembling formal mathematical/algebraic symbology, I would have to pass.

Funny how different minds think ... well ... "differently"

Ed, we seem to be similar thinker types, in the broadest sense, of course, for thinking styles, I suspect, are ultimately as unique as human beings.

As for the coin puzzle, congratulations, Ed. I got bogged down with the wrong suspicions - like: was there an emperor at the time? Was bronze used?

I couldn't bother with the mathematical puzzle, which only goes to show how strong my aversion is against word problems of that kind (thanks for providing the solution).

"mathematics and I" is a long and complicated story, too involved for the present comment.

At any rate, you are making, I think, the most important point in challenging the idea that "no creativity or innovation was required to solve" the analytic problem.

As for the main theme of the article: when I think I'm at my wit's end, taking a walk, or going shopping, or a night's sleep, work miracles with me. It is not so much a matter of fruitful destraction, it is just that my brain wants to be on its own for a while, so as to complete the solution. On my return or next morning I sit down and the solution pours forth out of me.

I got the criminal coin instantly. The age of Bob and his father required me to dust off both a pencil and the portion of the brain that used to do quite well in algebra. Happy to report it still works.

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