I hate when I start something and then think "you know, I bet someone's already done this and done it better than me", look and then find that its true.

I hate it more when it happens on the scale of hours or even minutes.

Programming is indeed humbling.

I have gotten to the point that if I find a problem that no one seems to be solving - I wonder if it is the wrong problem ... or at least improperly formulated.

I love it. That's the power of the internet. You can focus on solving of the problems that nobody has solved before

IFF you can find one, unsolved, within your own skill set.

While programming problems these days might not be so academic, or theoretical as they used to be, there are still plenty of things to solve. Why does this program do strange things, how can we glue these components together, how do I make this program do Y when it does X.

Yes, you can just look at open questions on SO

Found this...

http://mathworld.wolfram.com/RabbitSequence.html

The binary sequence produced from the Google doodle is listed as the "limiting sequence"

Go implementation of the doodle: https://github.com/taliesinb/tmachine