I think I might have found a way. I just stumbled over the Kiixa Faucet.

It pays you for solving captchas (Solve Media). 10 Satoshi per captcha and it has a limit of 2000 captchas per day. You just need an account on faucet hub. I also noticed, that sometimes it pays a bit more than 10 Satoshi. I'm not sure how long this might take, but after it you are at least half way through with your goal ;-)