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.
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by Robert Keim
by Luke James