I am confused by the distinction between solving a problem and checking the solutions for it if I ‘just estimate’ the solution. For example, if I am shown a picture of various scattered geometric figures, of slightly but obviously sometimes different areas, and asked how many kinds (classes?) of surface areas are there, I will squint and guess. If I am shown many such pictures, perhaps the accuracy of my guesses will improve. But what is it I am actually doing?
I am confused by the distinction between solving a problem and checking the solutions for it if I ‘just estimate’ the solution. For example, if I am shown a picture of various scattered geometric figures, of slightly but obviously sometimes different areas, and asked how many kinds (classes?) of surface areas are there, I will squint and guess. If I am shown many such pictures, perhaps the accuracy of my guesses will improve. But what is it I am actually doing?