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Questions about Reading Assignment:

Name the two most important things/concepts which you learned from the reading the chapter “The Architecture of Complexity”

1. give a one paragraph explanation why you consider these concepts important

The most interesting concept was that of problems solving. I think the most important asepct of problem solving is understanding that your solution may not be the best, nor even correct in some circumstances. If it is lacking or incorrect, however, it is best to learn from these mistakes. One of the primary sources of mistakes when dealing with a complex system is often just not understanding the problem, or placing false assumptions on the problem. This leads into what I feel was the other important idea presented in the chapter, the idea that often complex problems can be broken down into those which have already been solved. If you can look at a particular problem, and recognize patterns in the problem domain, you may be able to apply knowledge from another domain which has already solved a similar problem.

2. are the concepts relevant to your work, to your interest, …. – if yes, why?

Not that I can immediately see, although the difficulty equivalence of algorithms is certainly within the computer science realm.

Questions about The Importance of Representations in Design — The Mutilated “8x8” Matrix
remark: check the attached PDF file to see the graphical image

The Problem:

The associated PDF file shows you a mutilated “8x8” matrix (the two opposing corners cut out) and a domino block. One domino block covers exactly two fields of the “8x8” matrix.

Note: It is straightforward that one can use 32 domino blocks to cover a complete “8x8” matrix.

Question: Can one cover the mutilated “8x8” matrix with 31 domino blocks?

Remark: the major objective of this assignment is that you spend some effort trying to solve this problem and answering the questions below — it is not so important that you will succeed solving the problem!

Also: engage in some collaborative efforts solving it

Please do the following (please structure your answer accordingly — thanks):

1. try to find an answer to this problem! ‡ document briefly your thinking — including all the important intermediate steps and failing attempts (i.e., create a “think-aloud protocol”)

This seems to be a simple problem of evens vs odds. The dominos are even along one edge, and odd along another. Thus, if we lay them out in a line facing the same direction the line will either be even or odd in length. They must be facing the same direction so as to avoid single space holes in the grid, in which no domino would fit. The number of spaces in the modified grid is seven along each side. This will be impossible to fill since the dominos can be either even and even along both edges, or even and odd along each edge, but not odd and odd since when laying them in a line one edge of that line must be even.

2. which resources did you use to solve the problem?

I did not need any resource to solve it.

3. which process did you use?
4. which practice (of you or others) did you use?

I attempted to solve the problem by understanding fundamental patterns in the problem. There is definitely some error in this method as I can only think of so many ways to approach the problems, I may miss a configuration which is allowed by the rules but was not accounted for by my process.

5. could computers be useful to solve this problem?

A computer could potentially be programmed to test all configurations which adhered to the rules, possibly covering an input I would have missed on my own.

6. what have you learned solving the problem: in general and for our course?

I learned that the real difficulty is often not solving the problem, but defining what the problem is, and making sure your definition is accurate and does not leave a parameter unaccounted for.

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