As an ESL teacher, I was teaching my students some verbal idioms. I did not encounter any problems explaining to them the definition of each until we reached make up, think up vs come up with. I find that in certain context, they are interchangeable and in some they are not. When they are not, I have problems explaining to my students the reasons. I would really appreciate if someone can point me to the right direction.
think up an idea
come up with an idea
but we can't say make up an idea
think up an excuse
make up an excuse
come up with an excuse (seems to sound right, but I am not 100% sure. Can anyone help to confirm?)
come up with a solution
but think up a solution doesn't sound right
I have looked up in multiple dictionaries and most of them define think up with invent. I was guessing maybe think up is for inventions of original and only original ideas while come up with is for whether the idea is original or not. And is make up only for stories and excuses?