This is a Slitherlink puzzle.
S001 - Slitherlink
Why I listed this as special?
1. I made this entirely in head. I only use paper for testsolving it.
2. Shade the inner cells of the loop and try to find a pattern…
See if you can make your own puzzle that has this exact solution, with the least number of givens possible. In that puzzle, it’s 15… Can you do less?
After waiting for about two months, finally someone managed to complete the challenge. Let’s welcome Ours brun, which made a puzzle with a unique solution which is exactly identical to the above puzzle’s solution, yet only uses 12 givens as opposed to my 15. Go to this link for his(?) post that contains the puzzle.
For those that can’t read French (including me), here is the translation, accurate as Google Translate would do with some obvious grammar corrections:
This little Slitherlink [link to all posts in his(?) blog with Slitherlink tag] is a reply to this message [link to this entry] on the blog [of] chaotic_iak. But this does not prevent you to solve [this puzzle]! You see, he is truly charming.
A Chaotically Puzzling Blog 
What a charming pattern. 🙂
To answer your last question, here is a puzzle with the same solution, with 12 givens : http://ile-logique.blogspot.com/2011/06/ce-tout-petit-slitherlink-est-une.html
Verified to have a unique, identical solution. Great! You completed the challenge!
…nice idea. Let’s see whether this idea can make a good competition in this blog or not… 😉 (If you don’t know what idea, wait until I post it.)