Peter has a nice blog post about making his card. Check it out peterkagey.com/blog/2025/12...

I still do it, but they’re very low stakes—hardly worth more than a homework assignment.

A video of the pen plotter in action!

The sequence is defined as the following:

T(n,k) = length of longest carry sequence when adding k to n in binary representation, 1 ≤ k ≤ n (triangular array).

I asked a Code Golf Stack Exchange question about this too, if you want to read more.

codegolf.stackexchange.com/q/181203/53884

I can’t wait to see what comes next!

I like this a lot! I wrote a blog post about a similar shelf that I prototyped using cardboard.

I don't think there was too much behind that question—I think I was just curious if someone could figure out a rule.

I first got to walk a robot when I played with a similar demo from Chase Meadors, which you can see here.

A few years ago I wrote a related blog post about this!

(It's based on this fun video!)

See this playomino page!

(The technical question goes something like this: for each positive integer n, what is the smallest subgraph of the grid graph for which there exists a vertex partition whose resulting quotient graph is the complete graph K_n?)

In 2019, Ryan Lee—then a junior high student—found an example proving that you can connect all distinct pairs of integers in {1, 2, ..., 11} with a 34-vertex graph, which is the largest known term in OEIS sequence A278299. oeis.org/A278299

Thanks for the shoutout! I've recently added all of these problems to my website so that you no longer have to download the PDF.