This is a security problem for Project Euler and should have been disclosed to them as such. Dropping what amounts to a zero-day on their submission form is not acting in good faith.
The right way to go about this would have been to break the captcha, submit the problems, and then email them a polite writeup. Claim the glory after they fix it.
What are the "bad guys" going to do, create accounts and submit problem solutions...? There doesn't appear to be anything worth "attacking" here anyway, so I don't think this is a "security problem" at all.
Given that Google still uses text-based captchas in 2014, I think we can safely conclude that they are still state-of-the art. Of course Google's captchas are a little harder to defeat than these ones :)
1. ReCAPTCHA does a lot more than Project Euler's captchas... or to put it another way, the "Zero day" you're talking about would be worthless vs ReCAPTCHA: http://en.wikipedia.org/wiki/ReCAPTCHA#Security
2. Google requires a verified cell phone number for most of their services at this point, with the captha basically being a way to avoid spamming text messages
"Given that people still drive cars in 2014, I think we can safely conclude that the 1908 Ford Model T is still state-of-the art"
It's a dick move to be a griefer / enable grifers to a bunch of nice people. Lots of us knew you could do this; nobody else was a big enough ass to give script kiddies code.
There's no code provided, and not really any original research here either. Anyone that was trying to break such a simple captcha, and is able to understand this blog post, already has all the tools they needed to break it. Reading this blog post maybe would save someone half an hour of thinking about the problem.
And despite the previous commenter I don't see a problem with publishing a neat solution to a fairly cursory attempt to prevent automated submissions. If they care enough they can fix it, but the rather simplistic nature of their capcha implies they don't care much. shrug
The right way to go about this would have been to break the captcha, submit the problems, and then email them a polite writeup. Claim the glory after they fix it.