The e-ink (reader) side is the side that allows you to open and write on pdfs with the stylus using the built in programs (Reader, Journal etc.)
The lcd (tablet) side is the one that runs apps and is touch screen.

What I believe is the better set up is to have pdfs and solve on the e-ink (reader) screen. This is because it's not a touch screen and only responds to the pen. So it's easier for handwriting because you can rest your palm on the device, or hit the screen by mistake and not have it "write" something. That's how this should be used to maximum effect.

The LCD (tablet) side is a touch screen and any item can "touch" it to activate it. You can view pdfs on the tablet side through an app. the app I mentioned before was a lightweight photo editing app. (Not for touch ups, but more for adding smilie faces and mustaches on people, for example.) So if all you had was a jpg, then you could crudely add markings to "solve" the puzzle using that app, or I'm sure other apps that exist for making marks on photos.

But absolutely the best way to go about puzzle solving is to have pdfs and use the e-ink (reader) side.

Hope that makes sense.