The recreational mathematics I’m working on:
– integrated STEM missions with Raspberry Pi, robotics and physical computing

Much simpler than Zukei but still very useful for learning geometry:
– make a robot follow one of the geometrical shapes (an example with a parallelogram https://trinket.io/python/957faaf946)

I’ve also been obsessed with creating visualizations of concepts I’ve seen before but never really understood, like here: https://www.desmos.com/calculator/sfksyqhrxa. I find that these visualizations help me understand and remember a concept so much better than traditional algorithms and proofs ever do.

After doing a lot of new math over the break, I seem to have more empathy for my students as they struggle with material which is new to them but not new to me. So far today, the pace of my classroom has been much slower but at the same time much more productive.

Just a quick note also to express my thanks to Matthew Fahrenbacher, Jed, and Dan Anderson for devising Zukei puzzle solvers. They’re all rather different, each with its own set of strengths and weaknesses.

I wrote up the problem here. http://www.101qs.com/3899

If any follow the link and take a look, I would encourage you to do the problem first before watching Act3. Don’t miss the opportunity to make a mistake. Dan- thanks for the motivation to write it up.

Oh also, if you call “p” the probability of winning the coffee game, then your expected net gain is a function of p, say E(p). Your observations about there being 1 card and 1000000 cards amount to saying that E(1/2) > 0 and E(1/1000001) =2, so as you say, the Intermediate Value Theorem does not apply. But there IS a continuous function of p, with domain 0 < p < 1, which agrees with your expected value function, namely E(p) = 365p-1. You can apply the Intermediate Value Theorem to this function to obtain a p where your net gain is 0. Then since the function is increasing, you obtain the result you wanted without any loss of rigor. Incidentally, your wording indicates that I should bet if there are fewer than 365 cards in the bowl before I put your own in. Adding my own card changes the probabilities, so with that wording, we should use 364 as the cutoff, no?

How do we encourage our kids to express their excitement without banning one of the most concise written expressions of it? Maybe all them to do something like “n=365. Wow!”

This dovetails into more complicated situations that I bet many students might not realize are essentially similar — games of chance at a casino, playing the lottery, betting their teacher that two students in the room have the same birthday, etc. My favorite example here is the “Winfall Lottery” fiasco in MA, when three groups of people noted that they had a positive expected gain when playing on certain days and took advantage, making millions of dollars over many years. The group from MIT went further and used combinatorics to figure out how to fill out lottery tickets to minimize the variance on days they played, effectively removing any chance that they might lose money through bad luck. I saw Jordan Ellenberg give a wonderfully entertaining lecture about this — this appears to be the same lecture I saw: https://www.youtube.com/watch?v=2zLoxPEFwec

While some are straightforward, I’ve found many to be very challenging, especially trying to find solutions with the fewest operations. Even my young kids have enjoyed playing with the construction tools, drawing beautiful and/or crazily complex designs. In fact, for this open play, the simpler and more restricted interface is actually easier for them to use than Geogebra itself.

Another thing our family is considering recreational math: making a consistent effort to learn Go. So much to recommend this game and the life-and-death challenges are great logic puzzles. See here for a large collection of “beginner” puzzles: http://senseis.xmp.net/?BeginnerExercises