Anything can technically be the fourth dimension. The thing about dimensions is that they are open to be defined as needed. You can have four spatial dimensions, you can have ten spatial dimensions. You can have ten spatial dimensions and time being an 11th dimension. Its all up to whoever is defining the model being, well, modeled.
No, one is often saying the world i 3D and time makes it 4D. But there is nothing stopping you from having something in 4D where time isn't the fourth dimension.
That's how Einstein defined our world. Actually it's common to see 4 (and more) spatial dimensions in some science fiction novels, including the very famous one called "Three Body Trilogy"("San Ti" in Chinese).
So you would have to match up this puzzle with one being worked on by someone yesterday.