Do slight modifications to math questions generate derivative work?

Math questions published in a book are copyrighted as any other published text. Presumably, purely numerical questions are too.

Slight modifications to copyrighted works is usually considered derivative work, and if done without the author's permission is considered infringement.

My question is whether slighly modified math questions are considered derivative as well, or would it be original/transformed work, considering that merely changing the numbers in a math question would usually create a new problem to be solved. And TBH is probably how many, if not most, math questions for pedagogical purposes are generated.

e.g. Original

A tap on the top of a 20L tank fills it at the rate of 4 liters per hour, and another at the bottom empties it at 2 liters per hour. If both taps are open simultaneously, how long will it take to fill up an empty tank?

Modified

A faucet on the top of a 40L tanker fills it at the rate of 6 liters per hour, and another at the bottom empties it at 1 liters per hour. If both faucets are open simultaneously, how long will it take to fill up an empty tanker?

1 Answer

The basic questions are: 1. Are you copying? 2. Does/would a court agree that you are copying?

If you took the question as it is and modified it, that would usually be a derivative work. However, in science or mathematics, a tiny change can change a question completely. If someone writes “the earth rotates around the sun”, then “the sun rotates around the earth” is most likely not a derivative work.

So if you took an existing question, and changed it so that a different answer can be found in exactly the same way, I’d call it derivative and a court would likely do the same. If you changed the numbers in a way that totally changes the character of the question then I wouldn’t call it derivative but a court with a judge who is not a mathematician quite likely would.

It would be best not to start with an existing question. There is no copyright on the idea behind the question, so you can still develop your own from scratch. That would not be derivative- but you still have the problem of convincing a judge. In this case, there are similar questions found everywhere, so it would be very hard to prove which particular work yours is derived from.