They are insanely difficult. I actually wondered if I was being trolled (and my attempt at creating an account had itself been hell-banned and was supposed to be unsolvable). The audio captcha was not accepted either.
Whether the CAPTCHA tests are actually solvable, the goal, and the effort invested therein, is clearly to slow down the rate of throwaways per IP, per unit of time. Not test for humans.
It's not completely unreasonable to throttle an IP, and cap throwaways (read: ALL new accounts), to a maximum of 2 per 24 hours. It's also trivial to bypass with a different IP.
But yeah, those fucking image CAPTCHAS. Holy shit, they are definitely unsolvable at the current setting.
And the audio test, I'm six-sigma certain I got at least one in ten correct, and I was still refused.
Pretty sure, given HN's predilection for subtle counter-troll tactics, like hellbanning, that they're configured as a total lock-out, and not a turing test.
How do you get to it?
Generally, if you want to reach the mods/admins, send them an e-mail (hn@ycombinator.com). Way more reliable and quicker to get an answer.
No irony there.