That it may be more productive and less time consuming to attempt to prove that it is impossible to solve the MU puzzle than to attempt to solve it.

Just to be careful, I’m putting the rest below the fold.

I’ve already noticed that the only step that is capable of producing an I is step 2. I’ve also noticed that no matter how many times you multiply something by two, you never get a number that is divisible by three.

I suspect that if I use these observations in an attempt to prove the MU puzzle unsolvable, I will either succeed or find a solution.

EDIT: Okay, here’s what I think. I’m certain that the only way to end up with MU at the end is to create a string at some point that is M followed only by units of III and U. This means that you will have to have a sub-string containing a series of I’s at some point that is divisible by three, which I believe is impossible. As I said, the only way to increase the number of I’s in a string is Rule 2, which means you can never have a number of I’s within a string that is not 1 or a power of 2.

Therefore, I’m going to say that I think that the MU Puzzle is impossible to solve, especially in light of the discussion of that chapter, which makes it seem much more likely to me that Hofstadter wants us to use our pattern recognition skills to figure out that it’s impossible.

EDIT 2: In the interests of honesty, I hadn’t read past the car metaphor when I wrote any of the above. I really have turned procrastination into a competitive sport.