08-401/Homework Assignment 10 (and last!)

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Ok, it is time to acknowledge defeat. We've come to within a few hundred yards of the summit (just the few pages of the "Fundamental Theorem" handout, to be precise, and about two further lemmas from the book), the summit is clear in sight, yet we are not going to make it to the top. It is better now to retreat to base camp, and just talk a bit about where we have been and the little further, where we haven't been and will not go this time.

So next class will be a light class. I will tie a few loose ends and return a few debts, and perhaps briefly mention one of the key points we are still missing, but I will not attempt to push everything that is left into the remaining three hours. We will also discuss the final exam and the schedule leading up to it.

This assignment will likewise be light. Your only tasks are to read the "Fundamental Theorem" handout to get an overall impression of its content, and to have fun with the Just for Fun questions below. Nothing to submit and no due date, and HW grades will be computed using your best 7 out of 9 grades, rather than 8 out of 10 (in the About This Class document, I was careful to state that there wil be "about 10 homework assignments", and not "exactly 10").

Just for Fun

1. As done in class, prove that the following two "pentagonal rubik's style" combinatorial games are always solvable:

07-401-Pentagon Games.png

2. Which of the following three "hexagonal rubik's style" combinatorial games are always solvable?

07-401-Hexagon Games.png