To clean a shower room can be hard, if it has a lot limestone that is. Most sites will tell you vinegar and baking soda works wonders. Of all the sites I searched , no one said anything about old news papers.
Thats a trick my mother tought me. First you take a good shower to soften the dirt, then spray some lime stone remover. Leave for 10 min. Then use the paper on it. Its abrasive enuff to scrape and the print ink bounds with the dirt making it easier to scrub off.
Never try to clean the shower with the dirt rock hard dry. Usually it takes 2 or 3 times to get the shower spotless.