So, you used the Karnaugh map incorrectly. You need to wrap the cells around as in a cylinder.Unfortunately I've got to prove this works using Boolean Algebra only. I'm not allowed to use Karnaugh maps for this particular problem.
That's why I know the answer (having used Karnaugh to arrive there), but was struggling to see how to get to the same place with Boolean algebra alone.
by Robert Keim
by Luke James