What can you do if you can’t solve a math problem?
My advices are:
1. Read the problem word by word for several times until you really understand it.
2. Draw a diagram or a precise geometric figure. It will help you find out the relationship between the variations.
3. Change the numbers in the problem into some smaller ones. By considering those initial cases, try to find some patterns and inspiration. Finally, expand what you find.
4. List all the tactics or knowledge you learned which might help. Try them one by one.
5. Read some books or references and recall the things you learned. If you can’t solve a problem, there must exist an easier problem that you can’t solve. Make sure you understand it before you go back to the original problem.
6. Make a guess about the answer. Try to find contradictions in order to amend your solution.
7. Make discussions with your friends. Take turns to explain your thoughts and try to sum up in the end.
8. Eat some chocolate or go get some fresh air in the park. It will help you relax and improve your ability of thinking.
9. Write down the problems that you still can’t solve after using all the methods above. Think about them whenever you have time. Delete a problem when you solve it.
Never go to cram schools. You will lose your own thoughts!
(Translation by Scott Wang 王永光英譯 現就讀香港大學)