Testing abstract class throws InstantiationException

You've stated that BaseSudokuTest has an abstract method and is therefore abstract itself.

Assuming you are running your tests through BaseSudokuTest, Junit uses reflection to create an instance of your test class. You cannot instantiate abstract classes, whether directly or through reflection.

Move your abstract method to some other class. Your JUnit test class cannot be abstract.

Or rather run your HyperSudokuTest class. It will have inherited the @Test methods from BaseSudokuTest.