Serina Croll
Assignment 5
February 6, 2002
Solving the Mutilated 8x8 Matrix
1)Try to find an answer to this problem!
I tried, but did not succeed at fining an answer.
2)Document briefly my thinking – including all the important intermediate steps and failing attempts (i.e., create a "think-aloud protocol")
Initially looking at the matrix I believe that you can cover the entire matrix with 31 dominos because the two corner pieces have been removed so naturally you have the same amount of squares in the matrix as paired dominos. Assuming that I decide the only way to prove it is to try some different methods by trial and error. In my first attempt I start at the two corners that have been mutilated and just draw where dominoes might be placed. Then when I couldn't find the solution starting at each corner, I started from the edge going in, jut filling in the edges and progreessing towards the center. I knew the entire time that if I could fill certain squares of the matrix to leave the remaining squares so that they could be further broken down to one or more squares I would be able to fill out the matrix. I was never able to acomplish this first task, and thus failed at finding a solution.
Which resources did I use to solve the problem?
Mulitple print outs of the Matrix and a pencil
Which process did I use?
I used the process of trial and error.
Which practice (of you or others) did I use?
Trial and Error?
Could computers be useful to solve this problem?
Yes. I think that a computer with the diagram of the matrix and 32 domino images could be useful because a person could just move the pieces on the screen via the mouse. The image provided by the computer would make several steps of trial and error more feasible and enjoyable.
What have you learned solving the problem: in general and for our course?
What have you learned not being able to solve the problem: in general and for our course?
Some times you have to think outside the box. And being able to collaborate can help you solve problems.