I have a theory that the willow tree used to make Ron's true wand (Prisoner) wasn't just any tree- that it was the Whomping Willow on campus! It's like mid-term, the Willow was apologizing for beating the Weasleys' Anglia up: "Fine, Ron... you win. I'll let Ollivander make a wand out of me, and I'll make sure it chooses you."
So... bear with me. This is gonna be a doozy.
From 1938-45, Voldemort was at school and had a gang called (at least sometimes) the Knights of Walpurgis.
Now here's the thing. *Walpurgisnacht* from which the term "knights of Walpurgis" was probably derived, is the night from April 30-May 1.
Next the Battle of Hogwarts, the final battle in the 2nd Wizarding War, was the night of May 1 (c. 8:30) through the morning of the 2nd (c. 5:30 or 6). Did JKR mean to have the War decided the night directly after Walpurgisnacht?
There seem to be 2 major "schools of thought" about how to play an any-size balanced version of Rock, Paper, Scissors with 2n+1 elements.
Part 1: assign the numbers 0-2n (or 1-2n+1) to the elements.
1: (my primary) Now the players pull out two numbers A, B. If A=B, that's obviously a tie. If A=/=B and A > B, look at by how much they differ. If A-B is even, B wins, and otherwise A wins. (This also leads to a satisfying way to increase the n in the game by 1 at a time: add one element of minority parity that defeats exactly those of majority parity, then an element that defeats the new guy and all of like parity *to* it)
2: (probably more logical) Look at A-B mod/amod 2n+1. If the number is 0 or 2n+1 (depends on the range and which of those two it contains), that's a tie. If 0 < A-B mod 2n+1 <= n, A wins. If it's more, B wins.
How far does each "school of thought" let the average person go (in terms of n) while remembering the number/element mappings, before it just devolves into "what're the odds?"
If you pick 2 random natural numbers x & y, how often will l(x)l(y) (i.e. the product of the Calkin-Wilf terms with those indices) be less than 1? Upon intuition, the answer feels like it should be 50% but it's probably less.
If you're wondering about how this relates to Heronian triangles (where the sides and area are all integers), the half-angle tangents obey this formula with at least tu < 1. (The formula's the HAT form of A+B+C=180⁰) tu+uv+vt=1. You can rearrange it as follows to see that picking t & u forces v: 1-tu=v(t+u), or v=(1-tu)/(t+u). If you scale a regular Heronian triangle down by a factor of the circumdiameter, thus equating the sides and opposing sines, you can define the whole triangle in terms of t & u.
Actually 2:
In the 1976 single, which is the version of "Wreck" I'm referring to if I don't specify, is there exactly 29 of anything to match the 29 fallen sailors? The closest I got was that the lead guitar has that many "primary" bars in the song before "Lake Huron rolls, Superior sings..." where it and (if the drums are there) them are the only instruments really played.
What parallel mode of B major is the song in? We know by/on the words "to the lake" that it's either Mixolydian or Dorian (G# but A natural - "chip" of "Chippewa" is on A, "the" in "to the lake" on G#) but... does he ever sing a D or Eb? If so, which one? D natural means Dorian, Eb (D# in this context) means Mixolydian. In other words, if the 1 chord he used wasn't a sus2 and was a regular major/minor triad, which one would he have used? (The "does he sing either of these notes" question, D vs Eb, applies to here too as the middle note of the 1 chord)