This game is called Cursor * 10, the objective is to make it up to the 16th floor by solving puzzles in each floor, but some of them are cooperative puzzles and the only way to get through is with your own help!
You have 10 turns to control your mouse cursor, but your cursor dies after a certain time has passed, what you did in that turn gets recorded, though, so your own progress helps you advance to the next floor! It's pretty easy to understand once you play it! So far I've only made it to the 10th floor!
I hope you enjoy it!
Update: I'm now at floor 15 but can't seem to reach floor 16, if anyone finds out how to do it, please leave a comment!