Pattern Overlay Method (POM)

The Pattern Overlay Method, usually written POM, is a brute-force-adjacent technique that enumerates every possible placement pattern for a single digit across the grid. A "pattern" is a set of nine cells — one in each row, one in each column, three per box — where the digit could legally be placed without conflicting with the puzzle's existing givens or candidate restrictions. POM lists every valid pattern for the digit, then takes the union of cells where the digit appears across all patterns. Any candidate cell of the digit that doesn't appear in any pattern can be eliminated.

How the enumeration runs

For each of the digits 1-9, generate all possible "templates" — placement configurations that satisfy Sudoku's row/column/box constraints. For an unworked grid, there are 5,472,730,538 such templates per digit; for a partially-solved grid the count drops sharply, often into the dozens or low hundreds. The enumeration intersects with the candidate state: only templates compatible with the current pencil marks are kept.

Once the enumeration completes, POM's elimination is mechanical. For each cell, check every surviving template — does at least one place the digit there? If yes, leave the candidate. If no, eliminate. The same procedure runs for each digit independently.

Why it sits at the edge of "technique"

POM is technically a deduction — every elimination it fires is a logical consequence of the puzzle's rules — but it's also computationally heavy in a way other techniques aren't. The other named patterns (X-wing, AIC, ALS-XZ) are all specific logical patterns whose presence on the grid produces eliminations directly. POM enumerates every possible state and intersects them.

Some solver communities reject POM on the grounds that it isn't really a technique — it's just exhaustive search dressed up. Others accept it because the eliminations are valid and the procedure is well-defined. The middle position is that POM is a useful diagnostic for software solvers: when no human-recognisable pattern fires on a given puzzle state, POM tells you whether any eliminations remain to be found before falling back to true brute-force.

When you'll see it

You won't, manually. POM is impractical to run by hand on any puzzle harder than easy. Software solvers use it as a fallback when the human-recognisable techniques in their hierarchy run out, and as a benchmark for measuring puzzle difficulty (a puzzle "needs POM" if its only remaining eliminations come from pattern-intersection rather than from named patterns).

For a closely related technique that runs at the same conceptual level, see Templates.