Speaking from my own experience as teacher at German universities: If the professor cannot be bothered, then they believe the cheat sheet will not make a huge difference anyways. Even more so because four pages is already quite a lot. The professor is simply not into testing your memoization skills. So simply follow their instructions by the letter and you will be fine. But also be aware that investing all your time and effort only into preparing the "best possible" cheat sheet is probably not the best way to allocate your ressources. I'll try to explain to you why.

I think that cheat sheets are particularly common in math courses. Mathematicians do not value memoization pretty high. What's more important to them is the understanding of the concepts and the skills to perform computations and logical deductions. (And with regard to computations it is often considered most valuable that the correct algorithms are used; small errors in the computations typically result in only moderate score reductions.)

A typical exercise in such an exam is to perform Gaussian elimination on a small system of linear equations. A cheat sheet would not help you much if you have not thoroughly practiced the algorithm before the exams. Even if you put all steps of the algorithm onto the sheet, you will simply lose too much time when you try to reproduce it for the very first time.

Another example is computing an integral by substitution or by integration by parts. You can put these rules on the cheat sheet. (It is indeed a good idea because it is easy to get them wrong when one is nervous.) But you would hardly be able to apply these techniques without having developed an intuition on where and how exactly to apply them.

Writing a cheat sheet is a good idea nonetheless because the process of writing

1. helps with memoization;
2. is a good warmup (you can refresh your knowledge and load it into a region of your memory that can be quickly accessed by your "central processing unit");
3. gives you an overview of all the material, and it might tell you which topics might be worth more practicing.

Note that for all this to happen, it is crucial that you write you cheat sheet yourself. And it might be a good idea to do it in handwriting, not with the computer.

Also, having the cheat sheet with you during the exams is a good psycholgical trick and might help to lower your level of nervousness.

And remember: The best cheat sheet is the one onto which you don't have to look during the exams!

Speaking from my own experience as teacher at German universities: If the professor cannot be bothered, then they believe the cheat sheet will not make a huge difference anyways. Even more so because four pages is already quite a lot. The professor is simply not into testing your memorization skills. So simply follow their instructions by the letter and you will be fine. But also be aware that investing all your time and effort only into preparing the "best possible" cheat sheet is probably not the best way to allocate your ressources. I'll try to explain to you why.

I think that cheat sheets are particularly common in math courses. Mathematicians do not value memorization pretty high. What's more important to them is the understanding of the concepts and the skills to perform computations and logical deductions. (And with regard to computations it is often considered most valuable that the correct algorithms are used; small errors in the computations typically result in only moderate score reductions.)

A typical exercise in such an exam is to perform Gaussian elimination on a small system of linear equations. A cheat sheet would not help you much if you have not thoroughly practiced the algorithm before the exams. Even if you put all steps of the algorithm onto the sheet, you will simply lose too much time when you try to reproduce it for the very first time.

Another example is computing an integral by substitution or by integration by parts. You can put these rules on the cheat sheet. (It is indeed a good idea because it is easy to get them wrong when one is nervous.) But you would hardly be able to apply these techniques without having developed an intuition on where and how exactly to apply them.

Writing a cheat sheet is a good idea nonetheless because the process of writing

1. helps with memorization;
2. is a good warmup (you can refresh your knowledge and load it into a region of your memory that can be quickly accessed by your "central processing unit");
3. gives you an overview of all the material, and it might tell you which topics might be worth more practicing.

Note that for all this to happen, it is crucial that you write you cheat sheet yourself. And it might be a good idea to do it in handwriting, not with the computer.

Also, having the cheat sheet with you during the exams is a good psycholgical trick and might help to lower your level of nervousness.

And remember: The best cheat sheet is the one onto which you don't have to look during the exams!