[azim]

I tried breaking this captcha. Here are some experimental results and mathematics:

By applying the mathematics from the Birthday Attack (http://en.wikipedia.org/wiki/Birthday_attack), If an attacker is able to solve 15.8 million of the 180 million captchas, there will be a 50% probability that the attacker can beat the captcha.

I tried refreshing the page 10 times, generating a total of 100 captchas. Out of those, I observed 8 arithmetic problems which I entered into and solved using Wolfram Alpha. That gives roughly the 15.8m/180m necessary to break the captcha with 50% probability.

At 50% probability, again going back to the Birthday Attack mathematics, an attacker would need roughly 16.8 thousand tries before expecting a collision with one they could break.

This probability will increase if an attacker is able to successfully reverse-engineer more patterns.

Edit: thinking about this more after MichaelGG's comment, I think my math is incorrect. Either way, point still stands that Wolfram Alpha can successfully solve 8% of the captchas and other patterns should be solvable by other means too.

[MichaelGG]

Can you explain how the birthday paradox applies here?

Just looking at it simply, if you can solve 15.8 of 180, that means that for any given test you should have an 8.77% chance of solving it (6 tests for > 50%). What am I doing wrong?

Also, it looks like some of the other questions are easy to automate. Like "how many letters are in the word 'whatever'".

[baddox]

A Birthday Attack relies on the fact that even for some rare events (such as two random people having the same birthday), when there is a large opportunity to observe the rare event (such as 30 random people in the same room) it's actually quite likely to observe the event.