Note, looking into this is officially preparation for one of my fall classes. Work work work.

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Matthew Seymour has done more incredible work in service of the connection game Hex, this time in the form of a beautifully-implemented collection of 500 "white/black to play and win" puzzles of the sort that chess and go enthusiasts take for granted as study tools:

An uncommon sort of sliding block puzzle that I spent some time developing a little while ago. No browser-based version of this yet, just a screenshot from Mathematica.


It seems to me that there's a tendency to want to average by flat, as opposed to averaging by person. In that way, it reminds me of problems like "you cycle out at 10 mi/hr and back the same route at 24 mi/hr, what's the average speed for the round trip?"

Demystifying Beethoven's Große Fuge

(Personally I don't think it needs "demystifying," exactly, but anyway – if you want to spend 50 minutes working through the score, there you go)

And the lure of sitting back and watching the Blinkenlights while the computer searches for a construction is the most pernicious trap.

The back-and-forth between "Can I construct an object of type X?" and "Can I prove that there is no object of type X?" is the most delicious part of mathematics, I think.

Definitely what Minnesota needs today is some 75-mph winds and a few tornadoes to settle everybody's nerves.

Excited to start summer research with wonderful students, less excited about all the other things rushing in to grab up all the available time.

A nice page of recent writings about abstract strategy games (mostly connection games:
(Clicking the tags at the bottom of the page leads to many more good, unindexed articles)

Thanks to automatic captioning, I apparently gave a lecture on "Catalan numbers and snack permutations" last week.

For some reason, I feel that when the whole and only point of the question is "think about this reasoning," students pause and take some time to do that. If the question asks for a number, then it's like they have free license to skip the time-consuming "reasoning" step, multiply some things, get a number, and move briskly along to multiplying some different things in the next problem.

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A type of question that I incorporated into my 100-level discrete math course. I made about eight of these. I think it was a good addition. (They often functioned as a clue for the following question, which would entail coming up with one's own counting strategy for some problem)

Oh, I think I read about this. Weren't the soviets experimenting with ternary-based foxes in the late 1950s? I think one model was called the ВИКСУНЬ.

When I did a lot of road cycling, I often heard the mantra "Cheap – lightweight – durable... pick TWO."

Preparing my class stuff lately feels like "Good pedagogy – works online – can be prepared in time... pick TWO"

My students are taking a quiz with a counting question about hands of cards of a particular type. They have multiple attempts at the question with hints in between, and I can see the responses they've submitted. This gives me a fascinating problem of reverse-engineering the attempted strategies from the numbers that were submitted. It's instructive.

Elemenatry combinatorics lectures or textbooks tend to present mostly, or only, correct solutions to counting problems, which are easily seen to be correct. But when you're learning to count you'll spend most of your time looking at (your own) incorrect solutions and trying to figure out what's wrong with them. Or looking at your own solutions and trying to figure out whether they're correct or not. I dunno, maybe there's a moral there.

When I'm grading proofs by hand I usually run through the stack once marking any zeros or full credit ones and pulling them out, and keeping the ones that will get partial credit insertion-sorted as I go. Once I've seen the full spectrum of mistakes and misconceptions, I go back and assign the partial credit points.

This is tougher to do with electronic submissions.

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