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The beauty of the Karnaugh Map is that it has been cleverly designed so that any two adjacent cells in the map differ by a change in one variable. It's always a change of one variable any time you cross a horizontal or vertical cell boundaries. (It's not fair to go through the corners!)
Notice that the order of terms isn't random. Look across the top boundary of the Karnaugh Map. Terms go 00, 01, 11, 10. If you think binary well, you might have ordered terms in order 00, 01, 10, 11. That's the sequence of binary numbers for 0,1,2,3. However, in a Karnaugh Map terms are not arranged in numerical sequence! That's done deliberately to ensure that crossing each horizontal or vertical cell boundary will reflect a change of only one variable. In the numerical sequence, the middle two terms, 01, and 10 differ by two variables! Anyhow, when only one variable changes that means that you can eliminate that variable.
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