Here's a little game I made as a spiritual successor to Towlr and Babby of Towlr. Please bear in mind that this game is not a serious entry for the J4K, and was mostly made because of a joke around the Ludum Dare irc channel.

Towlr4k

If the sound doesn't work, there's a non-4kb version that includes the default java soundbank at:

Towlr4k (non-4k, with soundbank)

The idea behind Towlr is that you have to figure out the game and the goal itself. Thus, there will be no game description here. For some inspiration if you get stuck, the original two Towlr games can be found on Towlr.com. I do urge you to try out the online (flash) version of the first Towlr. It's an interesting puzzle game concept, and likely to leave you somewhat irritated until you figure out the trick.

Towlr.com

The game is much less than 4kb with no optimization, because of its simplicity. It was made rather quickly as I'm short on time for most of december.

I had a quick go.  So far I've not figured it out.  I'll try it again later.

Cheers, Tim.

Spoiler (strike-through to make it harder to read):

No, the sound does not affect the gameplay. That's why I could also provide a version without sound in 4kb.

EDIT: On a side note, I hope to also find the time to enter a more serious game before the contest ends.