Unlike a lot of grouping or partitioning problems, a K-map doesn't require every group to claim its own separate territory. The same cell can belong to two, three, or more groups at once in the final answer — and far from being a bug or a sign something went wrong, it's often exactly what a correctly minimized result looks like.
Why overlap doesn't cause double-counting
An SOP expression is an OR of its terms. OR only cares whether at least one term is true — not how many. If a cell is covered by two overlapping terms, both terms correctly evaluate to 1 for that input, the OR of "1 or 1" is still just 1, and the function's output for that cell is exactly as correct as if only one term covered it. Overlap changes nothing about correctness; it only affects which cells "belong" to which group conceptually, and that was never a constraint the algebra cared about in the first place.
A worked example: one cell, three groups
Take the majority function F(A,B,C) = Σm(3,5,6,7) — the same carry-out logic covered in the full adder example. Minimized:
| Term | Covers |
|---|---|
| BC | 3, 7 |
| AC | 5, 7 |
| AB | 6, 7 |
Minterm 7 appears in all three terms simultaneously. That's not a mistake to fix — all three groups are essential (each is the only one covering at least one of minterms 3, 5, or 6), and minterm 7 simply happens to sit in the overlap of all three. There's no smaller expression that produces the correct output for this function; the overlap here is a structural feature of the majority function, not something a "better" grouping would avoid.
When overlap is actually useful to look for
Beyond just being allowed, deliberately checking whether a cell can join more than one large group is often how you find the minimal answer in the first place. A cell doesn't have to be assigned to only its "best" group — if it validly belongs to two different maximal groups, both can be kept in the final answer if both turn out to be essential, exactly as in the example above.
What overlap is not
Overlap between groups is different from a single group being invalid. A group still has to be a proper rectangle of the correct power-of-two size on its own — overlap describes the relationship between separate valid groups, not a license to combine two groups into one irregular shape. See the shape rule specifically in Common Karnaugh Map Mistakes.
See every group's coverage, overlap included, directly in the Prime Implicant Analysis panel for any function you enter into the solver.