Problem solving my uncommon techniques include but not limited with:
• Hypothesizing if starting solution from the happy end …
(I would like to elucidate a bit more this approach on the following fresh example taken from real football game. In fact this draft description may be considered as evidence of my another “Following to instantly sparkling ideas” approach which have came to my mind immediately after one of the greatest fightbacks in Premier League history on Yesterday.
Many fans of football game may have watched and enjoyed British Premier League game of Newcastle Arsenal (February 5, 2011). Let’s suppose that we are problem solvers and have asked solving the following problem related to that game:
A.You are given to examine scenes some 1-2 minutes before the kickoff that match
B.You are given to examine scenes some 1-2 minutes after the game is over
And for both cases you are asked to try telling some events based on facts, of course, without watching game and having any other external information (Imagine that after game you see only score in the table without any details).
A. What can be said in language of mathematics for this situation?
It is only obvious (100%) in case of A that the score is 0-0. However there is no any 100 % probability what will be next scoring 1-0, 0-1 or 0-0 (will remain till the end of the game). All events (goals, yellow and red cards, penalties and etc.) that one may predict based on the statistical various analysis (historical previous games, tournament positions and etc.) will have more and less probabilities (0<X<1).
B. Now we are examining situation when everything within this game is over after certain times (90 minutes).
And we have been seeing only score 4-4 at the stadium table. From this now we can indicate that previous score was 4-3 or 3-4 (now it seems that there are 2 possible cases against 3 cases in situation of A)*.
However scrutinizing some other factors related to that game we can find little useful information which may consequently helpful to enrich our analysis
• 4-4 score approves the fact that it was very dramatic game which was not easy to predict prior to game (some probability less than 1)
• At the end of game you have noticed that there are 10 players of Arsenal which points out another 100% event (referee has showed a red card during the game). The chance of being red card before the match may have a certain probability definitely less than 1.
• More scrutinizing jubilation of Newcastle players, coaches and stadium audience consisted from mostly host funs with collaboration of disappointed Arsenal players and coaches shows the great probability that Arsenal may have lose its chance to win…, so now it is much great probability that previous score of the game Newcastle-Arsenal was 3-4 rather than 4-3. This situation has not analogue with the situation before the game.
Comparison of A and B cases are revealing that there are more helpful facts at the end of the game compared with the start of the game in order to try depict the course of events. In this specific example we were able to find probabilities of two events for our analysis: previous score and red card and may be as well some general information revealing the dramatism of game which may be translated in business terms like trend, profitability, volatility and etc.
Conclusion: Sometimes in reality it may be useful to hypothesize status after having solved problem and try to recover some picture of preceding events which may be possible, visible, and valuable while achieving that goal…
*-Moreover in general for scores when only one team is shooting goals like 1-0, 2-0, 3-0 and etc there is just one possible preceding score 0-0, 1-0, 2-0 (event has a probability equal to 1)
Thanks for your attention.
If this makes sense please let me know and I would try to evolve this viewpoint. )
• Conjunction of simple and complex solutions …
• Scrutinizing potential solution which at first glance seems as incredible …
• Following to instantly sparkling ideas as key for finding solution …
• Solving easy parts of problem may prompt solutions for further parts …
• Concentrating on ruling out the contradictions …
• Relying on time, information and fortune as possible remedies while problem looks hardly soluble ...
Artsvi Khachatryan's Problem Solving Skills:
Artsvi Khachatryan's Problem Solving Experience:
I have over 16 years of solid experience working on a wide range of economic issues, and I am well versed in the areas of Economic data and models in conjunction with macro analysis and projections.