classes are over now (i have no idea how well or poorly I did in PDE). i'm pretty relieved, although I'm sort of floating in this sur-reality where I only have to work. Last week I took off 4 days to study for my finals, I think that period of just waking up whenever and going to study got me into the habit of life without job-work. So I keep having to remind myself to go into work, it's such an afterthought.
My girlfriend is pretty great. We're making some progress at keeping our lives together despite the fearsome forces involved. I do need to do some laundry soon. I haven't quite finished introducing her to my friends, mostly due to their unavailability re: school or not. But this like many things will resolve as t goes to infinity.
I spent last night talking with my friend Justin. We talked a little about languages, as is our way, then I ran him a bit ragged with a computational math game (that my thoughtful girlfriend got me!), but the passion of our conversation was kenken.
After solving a few together, he thought of making one. Turns out making kenken is challenging (reminding me of my similar experiences making kakuros / cross-sums
). And once you overcome the challenge of being able to make a kenken, there is the added challenge of making one that can be solved (not to mention verifying (how?) that the solution is unique). I was able to make a 4x4, and two 6x6's. Justin tried and failed to make a 10x10, but was able to make a 6x6. Then we traded, tried to solve the 6x6's. We weren't able to solve them, and couldn't even make much headway. Herein was the discovery that making solvable kenken is difficult. You have to make specific design choices to make them possible to solve, and if you don't know what these design features are, then you probably won't accidentally include them. We'd just begun to discuss these features when the night was over and I had to head home (through the horrid black quiet coldness).
I'm inspired to think of kenken in general terms, an n by n grid, with digits 1 to n going in each block. how many possible arrangements? n^3 i think. now add in the sudoku aspect, only 1 to n in each column and row. how many possible arrangements?... i don't know. then add in the many subgroup arithmetic constraints, further reducing the number of arrangements. hopefully to 1, making the solution unique. how many single-block gimme's do you need in an n by n grid? how many double-block gimme's (where you know the two numbers but not the orientation)?... etc. It's fun to think about, and I'll have some time in the next few weeks to ponder it, and play and solve some kenken/kakuros.