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Jackson Fox Homework 5 Mutilated Matrix Could I do it? Nope... Whay not? It would seem to be an impossible problem. Simply put, with a full 8x8 matrix each dimension is evenly divisible by two, meaning each row and column can be filled with dominoes placeed either vertically or horizontally. However, with two missing (non-consecutive) squares, two columns and two rows and no longer be filled with 4 dominos aligned in a single direction. Instead, one domino would have to be placed that was rotated 90 degree to the others. Doing so forced the next row or column to do the same. At this point, each row or column becomes essentially one square shorter. (At this point I think that while the matrix has an even number of squares, this really isn't true. I could look at this as four smaller 4x4 grids, except now two of those 4x4 grids are broken and have odd numbers of squares. I can't fill this broken grids with the dominos. Since the two broken sub-grids aren't contigous (since the two togather WOULD have an even number of squares), I can't solve the problem.) What resources did I use? Nothing beyond the website, though I did peruse the other homeworks after I had come up with my "solution". What practice/process did I use? First I tried to reason out why I couldn't do it (since that was my intuition). After coming up with a somewhat resonable explanantion I tried a couple of times just to make myself feel better. Could a computer solve this problem? I think a computer could solve this problem, though it wouldn't do it very well. What did I learn solving the problem? My first though, was "what a strange assignment"... But I think I see that this problem is really on e that is best solved by resoning/intuition/guessing rather thean trial and error or brute force. Such a problem is exactly at the heart of this course, since computers have yet to "reason" well, we humans get to do it. And we humans could probably do this a lot faster with some help from other humans. I didn't have anyone around to work on the problem with, so I had to "collaborate" with the answers posted by the other students. Their thoughts helped me focus my own (which were a bit confused). What did I learn by not being able to solve the problem? I'm not so sure. I feel like I got quite a bit out of it in terms of understanding this course better, but I feel that was more a product of undergoing the process of solving the problem rather than not being able to solve it.
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