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

We really thought that the sections related to the Sources of Selectivity and Problem solving as a Natural selection were the most important concepts.

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

These concepts are very important because solving a problem begins by examining its state ( the look ) and then relating it to what has been seen before or relating it to an event seen in the life of the human being. Humans are adaptive creatures because they can remember and can relate new events to previous events and make the new events fit their lives. When solving a problem, a human being can only move so much if he doesn't have a feedback or previous experiences to related topics, and that's when the sources of selectivity becomes important as a concept, because it would make solving any problem so much easier and would make the path to the solution a lot easier.

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

They are relevant to our work and studies because it illustrates the importance of collaboration in any domain. These concepts ease the pain of looking for a solution that might be close to a person, but just doesn't appear because one was not exposed to it before, but a teammate was. It also encourages the work as a democratic team were everyone has an input in a certain product, rather than using the surgical team where only one person thinks and tries to find a solution and the others just execute.

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”)

We first tried different combinations of the domino block inside the matrix but it did not work, then after that, we tried to rearrange the shape of the matrix to make it in such a way that 31 blocks could fit in. After we tried in vain to do that, we had to use some design and analysis algorithm books to see if there are any algorithms to ease the job, but we could not find any. As a last resource, we went to google and tried to find how some people that tried to solve this problem before us went about their solution and what were there thoughts on it.

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

We used our brains, some past encountered algorithms, then finally turned to GOOGLE and

3. which process did you use?

We first tried different combinations of 31 domino blocks inside an 88 matrix, then we tried to rearrange the matrix to shape it to fit our combinations.

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

We used the implementation and analysis of algorithms related to like the domino's solitaire and Hidden squares.

5. could computers be useful to solve this problem?

Yes, they could be very useful to this problem through implementing the brute force algorithm. And if the brute force algorithm cannot solve it, then you can implement another algorithm that is specific to the domino block and matrices. But there is a big need for collaboration and gathering as many ideas as possible to get an algorithm to solve this problem.

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

7. what have you learned not being able to solve the problem: in general and for our course?

We have learned that although a problem could not be solved ( in our case ), collaboration made the process easier because we were able to discuss many ideas since one of us could see the problem from a different angle than the other, then we could combine our thoughts and the thoughts deducted from the tools we used into one solid and confident thought that the solution was unreachable in this case.