Reasoning to a Solution
     When we solve a problem we typically must not only find a solution but first form an understanding of the problem. This can involve deriving inferences from the problem statement as well as determining a way in which to represent or think about the problem. The figure below depicts the matchstick problem considered in the text as well as some of the possible reasoning that some mind might have moved through in solving the problem. The inferences enclosed in the black box were ideas that turned out to be irrelevant to the problem solution. Read through this material and see if you can identify the relevance of the the other ideas to representing and solving the problem. Also check if you had recognized all of the solutions shown here...if not, can you explain why you didn't find these as well?
 

   
 

     Animations of two of the above solutions. The subscript refers to the match stick that was moved.
     To the right is a solution that moves only two matches. This solution was submitted by a problem solver in Canada.  

 Assignment
     The example above of reasoning involved in solving the problem represents my (somewhat contrived) reconstruction of the way in which I thought about the problem. See if you can solve the additional matchstick problems that have been provided and create a reconstruction of what you thought about in solving them.

Matchstick Problems
© Charles F. Schmidt