Eight problems were given to each of $30$ students. After the test was given, point values of the problems were determined as follows: a problem is worth $n$ points if it is not solved by exactly $n$ contestants (no partial credit is given, only zero marks or full marks). (a) Is it possible that the contestant having got more points that any other contestant had also solved less problems than any other contestant? (b) Is it possible that the contestant having got less points than any other contestant has solved more problems than any other contestant?