Remember each match must jump over two matches, either a set of I I or an X, and the match may jump in either direction, to the left or the right.  There are many possible solutions.  The key to finding a solution is to visualize the end result of the five X's and the step that must be taken just before the end result is achieved.   Since a match must jump over two matches, the last step has to have a set { I X I } which would enable either the left or right match to jump over the middle X, as in step 4 above.  Once this set is seen, then it can be deduced that there must be sets of { I X I } in the intermediate steps to enable single matches to jump over the middle X to form a new X.

So, the solution is to work backwards, visualize the desired result, what the last step is to achieve that desired result, and the intermediate steps to get you there.  Many problems in business require this type of thinking.  As a simple example, almost all product development work would use this backwards method.  You start with the desired final product and its specifications, price, look, etc., and work backwards from the final product to see how to get there from your starting point.  Rarely, should you develop a product starting from what you have, and seeing what kind of product comes out at the end.
 

One Possible Solution for Ten Coins Problem
 

Move No. / Formation at Beginning - the two coins to be moved are in { brackets } and the empty bracket {   }  shows which end being moved to.	Formation after the Move
1.   X  O  X  {O  X}  O  X  O  X  O  {  }	X  O  X  O  X  O  X  O  O  X
2.   {  }  X  O  X  {O  X}  O  X  O  O  X	O  X  X  O  X  O  X  O  O  X
3.   {  }  O  X  X  O  {X  O}  X  O  O  X	X  O  O  X  X  O  X  O  O  X
4.   {  }  X  O  O  X  X  {O  X}  O  O  X	O  X  X  O  O  X  X  O  O  X
5.   O  {X  X}  O  O  X  X  O  O  X  {  }	O  O  O  X  X  O  O  X  X  X
6.   {  }  O  O  O  X  X  {O  O}  X  X  X	O  O  O  O  O  X  X  X  X  X   Solved!

There are many possible movements to solve this game, which is not as hard as it first appears.  Notice how with each move, you are increasing the number of doubles {O  O}  or  {X  X} in the ending formation.  To get to a desired objective, it's necessary to do tasks one at a time, but each task gets you closer to the desired objective.

Even though the process of solving the ten coins problem looks similar to the process of the ten matches problem, the visualization of how to solve the two are quite different.  In the ten matches problem, you can view the solution process backwards, that is, start with the desired result and work backwards towards a solution.  In the ten coins problem, the problem doesn't lend itself to that kind of a process.  You really just have to work your way through from the beginning formation and try to make progress at each step of the way, keeping in mind the desired result.  Most problems of a technical, engineering, or scientific nature require such an approach.  You see what you have, and you can visualize what you want, but to get there, you have to start from what you have, and try to improve one step at a time.

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