Brother, you and I are totally on the same page. I learned a ton, and since I never check the Discussions until I write successful code (at least on my tsql testbed), I was excited to see my own MS SQL code was nearly identical to yours in terms of logic, and I literally spent DAYS racking my brain around this, so seeing it was a huge relief.

Funny thing is, when I succeeded, I added comment lines to the code in my own notes with very similar commentary as yours. LOL!

(Note: Some of my code might have one or two redundant/extraneous items in the subqueries, as I would run my subqueries independently for visualization purposes prior to adding them to my main query, and so may have forgotten to remove extraneous subquery columns.)

/* select the desired columns from the two tables */
SELECT h.hacker_id, h.name, count(c.hacker_id)
FROM hackers h
JOIN challenges c ON h.hacker_id = c.hacker_id
GROUP BY h.hacker_id,h.name

/* check for rows matching the max poss score */
HAVING count(c.hacker_id) = (
    SELECT max(n.num) FROM (
        SELECT hacker_id, count(hacker_id) num
        FROM challenges
        GROUP BY hacker_id) n)

/* check for rows that match only distinct scores */
OR count(c.hacker_id) IN (
    SELECT w.num FROM (
        SELECT count(c.hacker_id) num
        FROM challenges c
        GROUP BY c.hacker_id) w
    GROUP BY w.num
    HAVING count(w.num) = 1)

/* order the results as directed */		
ORDER BY count(c.hacker_id) desc, h.hacker_id;

Side note: I'm not sure why, but for some reason I could not rename the original count(hacker_id) with an "AS c_count" alias like you did (in my case I wanted to use "numchal" for "number of challenges submitted"). When I would try to call back to it, I would get an error saying the column didn't exist (and obviously it did), or that I was trying to use it illegally in another aggregate function. I could only call aliases like that when they were defined in another table or subquery. Maybe that's a quirk of psql/PostGreSQL/pgAdmin?