On Mar 10, 2013, at 11:46 AM, Joe Niederberger <email@example.com> wrote:
>> I was looking for a strategy. > > I see only two strategies here (there may be others): > >  Look for a decision tree solution - that's the way I originally solved the problem. Evidently its the way you started. It works if you see it through. > >  Look for a "signature" function (may also be called > "trace" or "fingerprint".) > > All the rest is just details of working the problem, though they may be suggested by the strategy. > Noticing the forms of the logical assertions is just one of the things you do if your main strategy is "decision tree". I would have never said it that way when I first solved the problem, I would have just said "*this* is what I know after *that* weighing". But I noticed the form anyway. Its just paying attention.
Those aren't strategies Joe, those are template solutions, well, the second one is, the decision tree is a strategy but a brute force strategy. When I originally missed the fact that we didn't know which way the coin leaned, I applied a template, the binary tree. However, once you pointed out that we didn't know which way it leaned, I had to develop a strategy. When I compared 3 vs 3 I realized that I was wasting some of that comparison and that I needed to make each step count, that is what what got me to 4 coins versus 4 coins. At the same time I knew that the final step had to involve 3 coins or less, and if 3 then I also had to know which way the coin leaned. I even had a 3, 3, 2 arrangement in the middle step, and almost posted it, but realized I still had a problem with my middle step. That was about 15 minutes in, after that I couldn't fixe the middle step and gave up. Brute force is a strategy, but generally one that you reserve for last as it may be too time consuming or even impossible. Knowing the number of permutations involved and the uniqueness of that second step, I would say that you used some other guide other than just a decision tree. Something to prune the tree. Good problem solving, beyond template solutions, is making a science out of hunches.