So it seems that you are missing the point I am making. Mathematics is like magic. When some talk about magic they are talking about the tricks while a few talk about the art itself. I am talking about the art.
On Mar 13, 2013, at 1:01 AM, GS Chandy <firstname.lastname@example.org> wrote:
> Further GSC's post of Mar 13, 2013 7:43 AM (pasted below my signature for ready reference): > > The solution arrived at via the above strategy is seen (in part - the most important part is shown) at: > http://mathforum.org/kb/message.jspa?messageID=8575196 . > > GSC > ("Still Shoveling!") > > GSC posted Mar 13, 2013 7:43 AM >> Robert Hansen (RH) posted Mar 12, 2013 7:24 AM >> (GSC's remarks follow): >>> >>> On Mar 11, 2013, at 5:26 PM, Joe Niederberger >>> <email@example.com> wrote: >>> >>>> Now I have no idea what you are claiming. >>> >>> Let me ask you this. You don't see how there is an >>> attribute to this problem that when you go in one >>> direction you are losing ground and when you go in >>> another you are gaining ground or at least holding >>> your own (because this problem is pretty tight)? >> Many >>> problems have this attribute. That is the "problem >>> solving" strategy I am talking about. >>> >>> Bob Hansen >> GOT IT! >> >> I now understand that the strategy I had used for the >> '12-Coin Problem" (when I had nailed it at age 10 or >> 11 over half a century ago) was like so: >> >> Step A of strategy: >> When I tried one way, I gained ground. >> >> When I tried another way, I lost ground. >> >> Step B of strategy: >> So I chose the way that helped me gain ground. >> >> Step C: >> Again, I found that, >> - -- when I went one way, I gained ground. >> - -- when I went the other way, I lost ground. >> Once again, I chose the way that enabled me to gain >> ground. >> >> REPEAT from Step A. (ad infinitum if required). >> >> The problem was solved! >> >> Many thanks for these 'Helpful Hints on Strategy'. >> >> I do believe all is now clear? >> >> GSC >> ("Still Shoveling!")