Entirely abstract challenges - like chess playing or mathematics (but not formal logic for some unaccountable reason) - have mostly been unpleasant uphill battles for me, not few of which, mind you, I have won. Maybe that is why I like the somewhat unfair denigration (below) of analytic problem solving as mere exercise for the drudge, as opposed to the arty ingenuity required by insight problem solving, which latter I like to think a practice more up my street.

While I did not spent much time guessing, the fact remains, I did not even come close to finding the answer to the riddle of the criminal coin.

Analytic problems generally require people to “grind out a solution” by systematically working through the problem utilizing a consistent strategy. Here is a classic analytic problem: "*Bob’s father is 3 times as old as Bob. They were both born in October. 4 years ago, he was 4 times older. How old are Bob and his father*?" No innovation or creativity necessary to solve this problem; one simply has to work it out mathematically.

Insight problems, on the other hand, often initially mislead the solver. Finding the right answer requires the solver to abandon the original interpretation and seek alternatives. Insight problems often involve an "Aha!" moment where the answer comes all at once, rather than via a systematic, incremental calculation. Here is a classic insight problem: "*A dealer in antique coins got an offer to buy a beautiful bronze coin. The coin had an emperor's head on one side and the date 544 BC stamped on the other. The dealer examined the coin, but instead of buying it, he called the police. Why?"*

*The source.*

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"

Posted by: Ed Stevens | 03/07/2012 at 01:17 PM

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.

Posted by: Georg Thomas | 03/07/2012 at 02:09 PM

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.

Posted by: AngelaTC | 03/11/2012 at 12:25 PM