I did another Ludum Dare with my twin brother recently. Our submission was called Enshrine which is a game about a journey up a mountain to a shrine. The mountain is guarded by ancient golems which you sneak around.
The core mechanic is to move stone blocks from one place to another. You can see the golem's line of sight, and you move yourself and the blocks to get to the next part of the mountain. My brother did the 3D models and the design, which are one of the best things about the game and got a good amount of positive feedback. I did the programming and made some of the puzzles.
This creates a puzzle that is intended to feel similar to sneaking around Hyrule castle in Ocarina of Time, the N64 game. It ends up being a nice mechanism- it makes you think about the space and how the blocks are arranged.
We made this game with Unity, and it can be played in the browser or downloaded. However, the browser version has some visual issues, so the downloaded version is the recommended one.