Student or Learner
Both can and may are used to say that something is possible. I understand their differences are subtle. How about the following examples? Can they be replaced with ‘can’?
1. There can be no doubt that he is guilty.
2. Some packaging cartons can be stored flat.
3. Can he still be alive after all this time?
Can the ‘can’ be replaced with ‘may’ in the following examples?
1. The problem may be solved in a number of different ways.
You have yourself put it very nicely when you say the diferrence is subtle. We always need to see what is the intent when we use this words. We can interchange "can" and "may" in all the examples you have qouted BUT the intent would change, as
CAN: More definite (with less probability) and less polite
MAY: Less definite (may or may not) and more polite
So it depends on
1. What is the intent, and
2. Who are you speaking/writing this to
Because in Enlish respect lies in the modal verbs, eg can, could, may, etc.
I hope this make it clear.