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Joel Clawson

1. The two most important concepts I got out of the article were that most problems can be solved by dividing them up into simpler and smaller problems and that the subparts of the problem may not have anything to do with one another to solve the problem.

1.1 I find these concepts important because it changes how someone looks at a problem. If a person is given a large problem to solve or task to accomplish, they may get overwhelmed at first by how daunting their job appears. Once they dig into the problem they see that they can break it down into smaller problems and those problems into smaller manageable problems. These problems have simple solutions and when joined together solve the harder problem.

1.2 I do use these concepts when I program. Most programs are large complicated things, but they can be divided into modules that provide a certain functionality to the finished product. Each module can be divided into smaller modules and into classes, if using an object-oriented language. The classes can be further divided down into member functions and variables. So programs just get broken down into a collection of functions and variables that get combined together to form the finished program.

2.1 I don't believe there is a solution to the problem because there is not a way to divide up the matrix into rectangles such that all of the rectangles contain an even number of squares. There will always be two rectangles that have an odd number of squares.

2.2 The resources I used were a whiteboard and marker so I could easily make changes to the matrix.

2.3 The process I used was to divide up the matrix into rectangles that would be completely filled with dominoes. I would then divide up the rest of the matrix into smaller rectangles that would also be completely filled with dominoes. I always ended up with two non-neighboring squares empty which meant there was an extra domino that was not placed in the square.

2.4 See 2.3.

2.5 Computers could be useful to help solve the problem because they could quickly go through and try every possible positioning for the dominoes. It would be able to say that there is not a solution to the problem because it did try every potential solution, where I am just speculating from a pattern that seems to have appeared.

2.6 I did not find an answer to the problem.

2.7 Just because a problem can divided into smaller more manageable problems, it does not mean that a solution will be able to be found for all of the smaller problems or that the smaller solutions will be able to be combined to solve the larger problem. Also, it is not a trivial task to know how to divide up the problem into the smaller more manageable problems.

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