(*) By a theorem of Richard Savage (1994), if the numbers from 1-24 are partitioned into three sets of eight numbers like this, then at least one of the winning probabilities (R>G, G>B, or B>R) must be less than (√5-1)/2. Thus, if all three are to be equal, then 39/64 is the highest possible common value, and this partition achieves it.
If you're interested in the game of Hex, Matthew Seymour's online strategy book is the best one-stop guide to practical play that I know of (and it's not too easy to stumble across):
Snap Cube Puzzle: Snap cubes have a post on one side, and holes (into which a post can fit) on the other five sides. How many ways to build a 2x2x2 cube out of eight snap cubes such that (1) the entire structure is connected, and (2) all the posts are in the interior – no posts sticking out of the surface? (All the different structures look the same from the outside; the difference is in the orientation of the eight posts internally.)
@jsiehler Okay, that blog entry as promised: http://tpfto.wordpress.com/2019/04/24/on-constructing-an-elliptic-function-from-its-zeroes-and-poles/
What's the "most scalene" right triangle – that is, how should the edges be proportioned so that the minimum difference over all pairs of sides is as large as possible? Let's assume we've normalized so that the hypotenuse is 1 unit.
(If you enjoy the answer for right triangles, also try the problem for triangles with a 120-degree angle.)
Forty-seven problems in Peg Solitaire (not that the web needed another peg solitaire page, but anyway...)
A Mastodon instance for maths people. The kind of people who make \(\pi z^2 \times a\) jokes.
\) for inline LaTeX, and
\] for display mode.