I would like to know the legality of producing a solutions manual for say a mathematics textbook. I intend to work through the problems in the book, recording the steps with explanations on how I solved the problems. From my research on the topic, a solutions manual that was not created by the textbook manufacturer can be considered derivative work.
I intend to share the solutions with others after I am done. Is it legal if I share it for free? What if I sell it?
How close can I reference a problem from the textbook in my solutions manual. Does page, chapter, title, author and edition referencing scream copyright violation? What if I say this solution is "similar to problem**** in **** 4th edition"?
If I change the wording of the problem will that make it legal? I ask this because of SAT guides and sample problems from various publishers, each problem is very similar, but all the publishers haven`t been sued to the ground both by the CollegeBoard and the other publishers, what are they doing that keeps them legal? Also, I`ve come across online forums that have "homework help" forums where people post homework questions they need help with. For the most part, the problems listed are copied word-for-word. The problem is solved with explanations by one or many users, is this legal? How so? Gray area?
Let`s say the problem in the textbook is as follows:
"Mary is at the train station. If the train is 60 miles away and travels at 25 miles per hour, how long will Mary have to wait for the train to arrive?"
If I phrase a similar question in the my solutions manual:
This problem is very similar to Problem 17 in ****, this is how I solved it:
"Lily is at the airport on a nondescript island near the Arctic Circle. The plane she is waiting to catch is in Planktonville, Antarctica located a distance of 20 miles away. If the plane travels at a speed of 6000 miles per hour, how long will it take the plane to reach Lily"
<insert solution and explanations>
As you can see, ultimately the approach to solving the problem is identical, am I legal?